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:
Council (30 seconds each): Share your name, school and grade level(s) or course(s) with your table; How are you feeling this morning?
Make Sense of Tasks and Persevere Solving Them (SMP 1)
Implement tasks that promote reasoning and problem solving.
Effective teaching of mathematics engages students in solving and discussing tasks that promote mathematical reasoning and problem solving and allow multiple entry points and varied solution strategies.
Effective teaching of mathematics engages students in making connections among mathematical representations to deepen understanding of mathematics concepts and procedures and as tools for problem solving.
Summer Literacy and Mathematics Professional Learning June 5-9, 2017 Day 1 – Make Sense and Persevere
Jill Gough and Becky Holden
Today’s focus and essential learning:
We want all mathematicians to be able to say:
I can make sense of tasks and persevere in solving them.
(but… what if I can’t?)
Great teachers lead us just far enough down a path so we can challenge for ourselves. They provide us just enough insight so we can work toward a solution that makes us, makes me want to jump up and shout out the solution to the world, makes me want to step to the next higher level. Great teachers somehow make us want to ask the questions that they want us to answer, overcome the challenge that they, because they are our teacher, believe we need to overcome. (Lichtman, 20 pag.)
… designed to help students slow down and really think about problems rather than jumping right into solving them. In making this a routine approach to solving problems, she provided students with a lot of practice and helped them develop a habit of mind for reading and solving problems. (Flynn, 19 pag.)
Sentence-Phrase-Word helps learners to engage with and make meaning from text with a particular focus on capturing the essence of the text or “what speaks to you.” It fosters enhanced discussion while drawing attention to the power of language. (Ritchhart, 207 pag.)
However, the power and promise of this routine lies in the discussion of why a particular word, a single phrase, and a sentence stood out for each individual in the group as the catalyst for rich discussion . It is in these discussions that learners must justify their choices and explain what it was that spoke to them in each of their choices. (Ritchhart, 208 pag.)
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?
What if we reframe mistakes to be billed as opportunities to learn? If we truly believe in fail up, fail forward, fail faster, how do we leverage the quick bursts of failuremistakes struggle to propel learning in a new direction?
Struggle is not optional—it’s neurologically required: in order to get your skill circuit to fire optimally, you must by definition fire the circuit suboptimally; you must make mistakes and pay attention to those mistakes; you must slowly teach your circuit. You must also keep firing that circuit—i.e., practicing—in order to keep myelin functioning properly. After all, myelin is living tissue. (Coyle, 43 pag.)
How might we position each learner to work at the edge of their ability, reaching to a new goal, capture failure and turn it into skill?
Because the best way to build a good circuit is to fire it, attend to mistakes, then fire it again, over and over. Struggle is not an option: it’s a biological requirement. (Coyle, 34 pag.)
How might we establish a community norm that calls for a trail of mistakes to show struggle and evidence of learning? What if paying attention to mistakes is an essential to learn? How might we celebrate the trail that leads to success, to keep moving forward?
How might we target struggle so that it is productive? For what should we reach? What if expand our master coach toolkit to include a pathway to sense making and perseverance?
What if we target productive struggle through process? How might we lead learners to level up by helping them reach? When learners are thrashing around blindly, how might we serve as refuge for support, encouragement, and a push in a new direction?