Tag Archives: Brain-Friendly Assessments

Fluency: comprehension, accuracy, flexibility, and efficiency

No strategy is efficient for a student who does not yet understand it. (Humphreys & Parker, 27 pag.)

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

When we teach for understanding we want comprehension, accuracy, fluency, and efficiency. If we are efficient but have no firm understanding or foundation, is learning – encoding into longterm memory – happening?

We don’t mean to imply that efficiency is not important. Together with accuracy and flexibility, efficiency is a hallmark of numerical fluency. (Humphreys & Parker, 28 pag.)

What if we make I can make sense of problems and persevere in solving them and I can demonstrate flexibility essential to learn?

SMP-1-MakeSensePersevere

Flexibility #LL2LU

If we go straight for efficiency in multiplication, how will our learners overcome following commonly known misconception?

common misconception: (a+b)²=a² +b²

multiplication_flexibility

correct understanding: (a+b)²=a² +2ab+b²

The strategies we teach, the numeracy that we are building, impacts future understanding.  We teach for understanding. We want comprehension, accuracy, fluency, and efficiency.

How might we learn to show what we know more than one way? What if we learn to understand using words, pictures, and numbers?

What if we design learning episodes for sense making and flexibility?


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.

Flexibility and sense-making to build confidence and long-term memory

In his TEDxSonomaCounty talk, The Myth of Average, Todd Rose (@ltoddrose) challenges us to consider and act to leverage simple solutions that will improve the performance of our learners and dramatically expand our talent pool.  (If you’ve not seen his talk, it is worth stopping to  watch the 18.5 minute message before reading on.)

There are far too many students who feel like they are no good at math because they aren’t quick to get right answers. (Humphreys & Parker, 9 pag.)

Efficiency must not trump understanding.  How often do we remember the foundation once we’ve mastered “the short cut?” Were we ever taught the foundation – the why – or were we only taught to memorize procedures that got to an answer quickly?

Of course, students must be able to compute flexibly, efficiently, and accurately. But they also need to explain their reasoning and determine if the ideas they’re using and the results they’re getting make sense. (Humphreys & Parker, 8 pag.)

How might we design and implement practices that help our young learners make sense of what they are learning?  In Brain-Friendly Assessments: What They Are and How to Use Them, David Sousa explains how necessary sense-making and meaning are to transfer information from working memory into long-term memory.

The brain is more likely to store information if it makes sense and has meaning. (Sousa, 28 pag.)

Dr. Sousa continues:

We should not be measuring just content acquisition. Rather, we should be discovering the ways students can process and manipulate their knowledge and skills to deal with new problems and issues associated with what they have learned.  (Sousa, 28 pag.)

The first chapter of Making Number Talks Matter highlights the importance of number talks.  We want our young learners to develop flexibility and confidence working with numbers.

Listen to Ruth Parker and Cathy Humphreys discuss Number talks:

From Jo Boaler’s How to Learn Math: for Students:

…we know that what separates high achievers from low achievers is not that high achievers know more math, it is that they interact with numbers flexibly and low achievers don’t.

What if we take action on behalf of our young learners?  What if we offer multiple pathways for success?

How might we dramatically expand our talent pool?


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.


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.