Monday, March 30, 2015

Classes should do hands-on exercises before reading and video, Stanford researchers say

The researchers drew on data gathered from students using the BrainExplorer, a tabletop tool that simulates how the human brain processes visual images.

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Tuesday, March 24, 2015

Courageous Conversation: Formative Assessment and Grading

With all the education action around Standards-Based Instruction, Understanding By Design, Assessment for Learning, Grading for Learning, Project-Based Learning, Competency-Based Instruction and more, we need to have a frank conversation about formative assessment and grading.

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Formative Assessment Is Transformational!

I think formative assessment is one of the single most important things that teachers can do -- and already do -- for their students. In fact, great teachers use formative assessment whether or not they know it.

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Friday, March 6, 2015

As a mathematics instructional coach, I've found the most difficult part of my job is getting teachers to understand the shift in instructional strategies that are supposed to accompany the Common Core math standards.

Gone are the days when students practice a single solution method on 20 different problems. Instead, students are encouraged to find 20 different solution methods for solving a single problem.

I have found that the easiest way to get teachers to understand this new way of approaching instruction is through Number Talks. I see Number Talks as the gateway drug to Common Core. If I can get a teacher to do Number Talks three times a week with her class, then she is 90% of the way to fully understanding the instructional shifts suggested by the new standards.

(It is important to understand that the standards don't explicitly prescribe too many specific instructional strategies, there is a general tone throughout the standards that we are to be teaching for deep understanding rather than just a superficial ability to do calculations.)

What is a Number Talk?A Number Talk is a five to fifteen minute discussion in which students verbally share their mathematical thinking as the teacher records the process on the board for everyone to see. They provide structured practice for mental math and promote the value in using mental math to compute. Number Talks teach the importance of being flexible with numbers and using a variety of strategies for computation.

Number Talks are implemented during the "warm-up." The problems and numbers use in the number talks are designed to elicit certain strategies that focus on number relationships, place value, and properties. As students explain and defend solutions, they will have an opportunity to collectively reason about solutions and to make connections between key mathematical structures. These number talks are a key component for students to develop flexibility with number.

What are the benefits of doing Number Talks?
  • Encourages math communication from all students
  • Provides structured practice for mental math
  • Promotes the value in using mental math to compute
  • Promotes the importance of being flexible with numbers
  • Using a variety of strategies for computation
One school district did nothing other than implement Number Talks in their classrooms. After only two years, student achievement in mathematics increased dramatically.

Scores on TOMA-2BeginningAfter 2 years
Below Average
Above Average23%36%
Superior /
Very Superior

Finally, the purpose of this blog postTwo barriers to doing Number Talks that I have heard teachers mention are
  1. What problem should I use for a Number Talk?
  2. What do I do if I don't understand the method a student is sharing?
To barrier Number 1...use ANY problem that you want. I tend to focus on addition, subtraction, multiplication, and division of whole numbers, since I am a K-5 math coach. Fractions, however, would also be a fine source of problems to do for Number Talks.

To barrier Number 2...who cares? Laugh with the class. Play dumb. Tell the student to repeat herself. Ask another student who does understand to "translate" for the rest of the students in the audience. Ultimately, if you don't understand the method, this is an opportunity for the student to find a better way to explain him/herself. It is also a great opportunity for you to model what it looks like to have a Growth Mindset.
I recently created a website ( to make it even easier for teachers to implement Number Talks.

At, teachers can choose to use the daily problem posted, or any of the other questions in the archive. (The problem does not need to relate in any way to the math topic that will be taught in the "regular" lesson.)

Once you have finished the Daily Number Talk routine, DON'T erase your board until you've taken a picture of all or part of your number talk solution methods. Then Tweet your photo to the microhashtag listed on the problem. Your photo will show up at the bottom of the page in a couple of minutes.
((( What is a microhashtag? A microhashtag is a very narrowly defined conversation (such as "17 + 14") that is directly related a web page such that the Tweets are embedded onto a web page. )))

I am hoping that not only will students be talking about the mathematics within their daily Number Talk, but teachers will also talk with one another about the awesome solution methods their students came up with. By teachers sharing their experiences, we can all grow (students and teachers alike) to become better mathematicians.

What do you think? Is this silly?