Yesterday, I had the privilege of attending a session at GISA on Implicit Bias facilitated by Trinity’s very own Gina Quiñones (@lillian_gina) and Lauren Kinnard (@LaurenKinnard).
Lauren and Gina began the session by setting norms, challenging us to level up from a safe space to a brave space. How might we dare to be brave enough to express what we think and feel? What if we listen to others to learn?
They challenged us to consider how might we turn our own cultural collisions into more meaningful connections and shared the following TED talk.
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?
If we go straight for efficiency in multiplication, how will our learners overcome following commonly known misconception?
common misconception: (a+b)²=a² +b²
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?
Continue the pattern: 18, 27, 36, ___, ___, ___, ___
Lots of hands went up.
18, 27, 36, 45, 54, 63, 72 Yes! How did you find the numbers to continue the pattern?
S1: I added 9. (Me: That’s what I did.)
S2: I multiplied by 9. (Me: Uh oh…)
S3: The ones go down by 1 and the tens go up by 1. (Me: Wow, good connection.)
Arleen and Laura probed and pushed for deeper explanations.
S1: To get to the next number, you always add 9. (Me: That’s what I did.)
S2: I see 2×9, 3×9, and 4×9, so then you’ll have 5×9, 6×9, 7×9, and 8×9. (Me: Oh, I see! She is using multiples of 9, not multiplying by 9. Did she mean multiples not multiply?)
S3: It’s always the pattern with 9’s. (Me: He showed the trick about multiplying by 9 with your hands.)
Without the probing and pushing for explanations, I would have thought some of the children did not understand. This is where in-the-moment formative assessment can accelerate the speed of learning.
There were several more examples with probing for understanding. Awesome work by this team to push and practice. Arleen and Laura checked in with every child as they worked to coach every learner to success. Awesome!
I was so curious about the children’s thinking. Look at the difference in their work and their communication.
By analyzing their work in the moment, we discovered that they were seeing the patterns, getting the answers, but struggled to explain their thinking. It got me thinking…How often in math do we communicate to children that a right answer is enough? And the faster the better??? Yikes! No, no, no! Show what you know, not just the final answer.
My turn to teach.
It is not enough to have the correct numbers in the answer. It is important to have the correct numbers, but that is not was is most important. It is critical to learn to describe your thinking to the reader.
How might we explain our thinking? How might we show our work? This is what your teachers are looking for.
The children gave GREAT answers!
We can write a sentence.
We can draw a picture.
We can show a number algorithm. (Seriously, a 4th grader gave this answer. WOW!)
But, telling me what I want to hear is very different than putting it in practice.
It makes me wonder… How can I communicate better to our learners? How can I show a path to successful math communication? What if our learners had a learning progression that offered the opportunity to level up in math communication?
What if it looked like this?
I can show more than one way to find a solution to the problem. I can choose appropriately from writing a complete sentence, drawing a picture, writing a number algorithm, or another creative way.
I can find a solution to the problem and describe or illustrate how I arrived at the solution in a way that the reader does not have to talk with me in person to understand my path to the solution.
I can find a correct solution to the problem.
I can ask questions to help me work toward a solution to the problem.
What if this became a norm? What if we used this or something similar to help our learners self-assess their mathematical written communication? If we emphasize math communication at this early age, will we ultimately have more confident and communicative math students in middle school and high school?
What if we lead learners to level up in communication of understanding? What if we take up the challenge to make thinking visible? … to show what we know more than one way? … to communicate where the reader doesn’t have to ask questions?
How might we impact the world, their future, our future?
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:
How might we design flexible spaces for learning? This is a current question in education. I wonder, however, if we are thinking deeply enough about this question. I hope that we will take up the challenge of thinking about learning spaces in more ways than furniture.
How might we design to leverage simple solutions that will improve the performance of our learners and dramatically expand our talent pool?
Don’t miss this compelling talk from high school dropout turned Harvard professor and consider how we might change and redesign to address the size differences of all learners.
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.
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:
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.
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:
After the class developed the learning progression:
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?