Tag Archives: 2nd Grade

Number Talks: how AND why

Listening informs questioning. (Berger, 98 pag.)

How do we know learning has occurred? How do we know how learning has happened? What if we pause and listen to learn?

If both sense and meaning are present, the likelihood of the new information getting encoded into longterm memory is very high. (Sousa, 28 pag.)

How would you add 39 to 67? Would you use the traditional algorithm? Would you need paper? How might we teach flexibility, sense making, and numeracy to build fluency and confidence?

Number talks are about students making sense of their own mathematical ideas. (Humphrey & Parker, 13 pag.)

How might we seize the opportunity to confer with our learners to see if they are making sense of what is being taught?

This is the challenge – and joy – of teaching by listening to students. (Humphrey & Parker, 13 pag.)

If interested in additional examples of number talks, both the how and the why, listen to Jo Boaler and her students from the Stanford Online MOOC How to Learn Math: For Teachers and Parents.

Do we believe our learners – every one of them – are capable of developing proficiency in mathematics?

How might we show what we know more than one way?

How might we continue to send the message I believe in you and mean it?

What if we listen to learn?


I am grateful to Kristin Gray (@MathMinds) and Crystal Morey (@themathdancer) for their leadership and facilitation as a dozen #TrinityLearns faculty participate in an online book club (#mNTmTch) for Making Number Talks Matter: Developing Mathematical Practices and Deepening Understanding Grades 4-10 along with over 600 educators across the globe.


Berger, Warren (2014-03-04). A More Beautiful Question: The Power of Inquiry to Spark Breakthrough Ideas . BLOOMSBURY PUBLISHING. Kindle Edition.

Humphreys, Cathy, and Ruth E. Parker. Making Number Talks Matter: Developing Mathematical Practices and Deepening Understanding, Grades 4-10. Portland, ME: Steinhouse Publishers, 2015. Print.

Sousa, David A. Brain-Friendly Assessments: What They Are and How to Use Them. West Palm Beach, FL: Learning Sciences, 2014. Print.

Empower learners to deepen their learning

How might we empower learners to deepen their understanding?

After creating and administering common assessments, the next question is perhaps the most challenging: “Are students learning what we think they are supposed to be learning?” (Ferriter and Parry, 75 pag.)

What if our learners are grasping the content, but they are struggling to communicate what they know and how they arrive at a conclusion?

How might we make our expectations clear? What if we empower our learners to take action on their own behalf?

What if our culture embraces the three big ideas of a PLC?

Learning is our focus.
Collaboration is our culture.
Results guide our decisions.

Our #TrinityLearns 2nd grade team sat down together last week to analyze the results of the most recent common assessment.  While our young learners are grasping the basic concepts, we want more for them. We want confident, flexible thinkers and problem solvers.  We want our learners to show what they know more than one way, and we want strong clear communication so that the reader can follow the work without to infer understanding.

Teams at this point in the process are typically performing at a high level, taking collective responsibility for the performance of their students rather than responding as individuals. (Ferriter and Parry, 77 pag.)

As a team, these teachers sorted their students’ work into four levels, shared artifacts of levels with each other, and planned a common lesson.

Laurel Martin (@laurel_martin) explained to our children that the artifacts they analyzed were not from their class and that they belonged to a class across the hall.

Here’s the pitch to the students from Sarah Mokotoff’s (@2ndMokotoff) class:

Don’t you just love the messages: Be like scientists. Make observations. Offer feedback on how to improve.

Here’s what it looked like as the children analyzed artifacts from another 2nd grade class:

Once the analysis was complete, our teachers facilitated a discussion where the children developed a learning progression for this work.

From Kerry Coote (@CooteMrs):

We created these together after looking at student work samples that were assigned at each level. Our kids were so engaged in the activity; they were able to compare and give reasons why work was at a level 3 versus a level 4. It was really good to see! I believe this will empower them to be deeper thinkers and gradually move away from giving an answer without showing their thinking and work.

Here’s what the students in Grace Granade’s (@2ndGranade) class developed:

IMG_8439

More from Kerry Coote:

After we helped them develop the learning progression, we conferenced with each child looking at their math assessment. They  automatically self-assessed and assigned levels for their thinking. Many scored themselves lower at first, but the activity of crafting the learning progression helped in making sense of explaining their thinking! Today in math a boy asked me – “so Mrs. Coote, what are those levels again? I know the target is Level 3, but I want to use numbers, words, and pictures to get to level 4.”  It is all coming together and making sense more with these experiences!

In their morning meeting the next day, one of Kathy Bruyn’s (@KathyEE96) learners shared the poster she made the night before.

Don’t you love how she explained the near doubles fact and her precise language?  Wow!

Since we focus on learning and results, this team offered learners an opportunity to show growth.

From Samantha Steinberg (@spsteinberg):

This is an example of leveling up after looking at our assessment.  Initially, [he] used the learning progression to rate his work at level 3.  After reading my feedback, he added words to his next attempt to show his additional thinking.

Before the class developed the learning progression:

Screen Shot 2015-10-01 at 8.08.58 PM

After the class developed the learning progression:

Screen Shot 2015-10-01 at 8.09.13 PM

Can you see the difference in this child’s work, understanding, and communication?

A growth mindset isn’t just about effort. Perhaps the most common misconception is simply equating the growth mindset with effort. Certainly, effort is key for students’ achievement, but it’s not the only thing. Students need to try new strategies and seek input from others when they’re stuck. They need this repertoire of approaches—not just sheer effort—to learn and improve. (Dweck, n. pag.)

Kudos to our 2nd grade team for reaching for the top stages of  the seven stages of collaborative teams! Learning is our focus. Collaboration is our culture. Results guide our decisions.

How might we continue to empower learners to deepen their understanding?


Dweck, Carol. “Carol Dweck Revisits the ‘Growth Mindset’” Education Week. Education Week, 22 Sept. 2015. Web. 02 Oct. 2015.

Graham, Parry, and William Ferriter. Building a Professional Learning Community at Work: A Guide to the First Year. Bloomington, IN: Solution Tree, 2010. Print.