At the 27th Annual KSU Conference on Literature for Children and Young Adults where the theme was Reimagining the Role of Children’s and Young Adult Literature, I presented the following 50-minute session on Tuesday, March 20, 2018.
Mathematizing Read Alouds
How might we deepen our understanding of numeracy using children’s literature? What if we mathematize our read-aloud books to use them in math as well as literacy? We invite you to notice and note, listen and learn, and learn by doing while we share ways to deepen understanding of numeracy and literacy.
Let’s debunk the myth that mathematicians do all work in their heads. Mathematicians notice, wonder, note, identify patterns, ask questions, revise thinking, and share ideas. Mathematicians show their thinking with details so that a reader understands without having to ask questions.
What if we pause during read-alouds to give learners a chance to analyze text features, to notice and wonder, to ask and answer questions in context?
How might we inspire and teach learners to make their thinking visible so that a reader understands?
Here’s my sketch note of the plan:
Here are more of the picture books highlighted in this session:
I can describe or illustrate ow I arrived at a solution so that the reader understands without talking to me?
Isn’t this really about making thinking visible and clear communication? Anyone who has taught learners who take an AP exam can attest to the importance of organized, clear pathways of thinking. It is not about watching the teacher show work, it is about practicing, getting feedback, and revising.
Compare the following:
What if a learner submits the following work?
Can the reader understand how the writer arrived at this solution without asking any questions?
What if the learner shared more thinking? Would it be clearer to the reader? What do you think?
How often do we tell learners that they need to show their work? What if they need to show more work? What if they don’t know how?
How might we communicate and collaborate creatively to show and tell how to level up in showing work and making thinking visible?
How might we grow in the areas of comprehension, accuracy, flexibility, and deeper understanding if we learn to communicate clearly using words, pictures, and numbers?
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?
I wonder if, when the house is finished, we forget the foundational infrastructure required for function. How does water get into and out of my house? Who ran the wires so that our lamps illuminate our space? Who did the work, and what work was done, prior to the slab being poured?
When we recall a basic multiplication fact, it’s like flipping a light switch in our house. The electrical wiring allowing us to turn on the light is linked to sound, safe, and deeply connected infrastructure. (K. Nims, personal communication, August 30, 2015)
Just like the light switch is not part of the foundation, memorization of multiplication facts is also not foundational. It is efficient and functional. Efficiency must not trump understanding.
We need people who are confident with mathematics, who can develop mathematical models and predictions, and who can justify, reason, communicate, and problem solve. (Boaler, n. pag.)
Students who rely solely on the memorization of math facts often confuse similar facts. (O’Connell, 4 pag.)
Students must first understand the facts that they are being asked to memorize. (O’Connell, 3 pag.)
What if we have forgotten all the hard work that came prior to the task of memorizing our multiplication facts?
Do we remember learning about multiplication as repeated addition? Have we forgotten the connection between multiplication, arrays, and area?
Conceptual understanding of multiplication lays a foundation for deeper understanding of many mathematical topics. Memorizing facts denies learners the opportunity to connect ideas, exercise flexibility, and interact with multiple strategies.
The goal is to have confident, competent, critical thinkers. Let’s remember that a strong foundation has many unseen components. What if we slow down to develop deep understanding of the numeracy of multiplication?
Second, going slow helps the practitioner to develop something even more important: a working perception of the skill’s internal blueprint – the shape and rhythm of the interlocking skill circuits.” (Coyle, 85 pag.)
How might we serve our learners by expecting them to show what they know more than one way?
[learners] may be self-censoring their questions due to cultural pressures. (Berger, 58 pag.)
What are the cultural norms in our learning community around asking questions? Who has permission to ask questions?
But this issue of “Who gets to ask the questions in class?” touches on purpose, power, control, and, arguably, even race and social class. (Berger, 56 pag.)
If learners are self-censoring their questions because of cultural pressures, who really has permission to ask questions?
How might we create space and opportunity for additional voices to contribute questions? What if we leverage tools – technology, protocols, strategies – to offer every learner new ways to have a voice?
What would it look and sound like in the average classroom if we wanted to make “being wrong” less threatening? (Berger, 50 pag.)
What is to be gained from using feedback loops as a way to make the possibility of “being wrong” less threatening?
If learners are self-censoring their questions because of cultural pressures, what actions should/can/will be taken?
Chapter 2 is full of interesting, important questions and ideas to ponder.
Why do kids ask so many questions? (And how do we really feel about that?) Why does questioning fall off a cliff? Can a school be built on questions? Who is entitled to ask questions in class? If we’re born to inquire, then why must it be taught? (Berger, 39 pag.)
I have many notes in my book. I am part of a cohort reading this book. I know that others will highlight and help discuss additional ideas from this chapter.
A doodler is connecting neurological pathways with perviously disconnected pathways. A doodler is concentrating intently, sifting through information, conscious and otherwise, and – much more often than we realize – generating massive insights. (Brown, 11 pag.)
How might we test this? What if we engage with our curriculum to experience connecting disconnected pathways, to generate insights, to make thinking visible?
It is the relationship between the teacher, the student, and the content – not the qualities of any one of them by themselves – that determines the nature of instructional practice, and each corner of the instructional core has its own particular role and resources to bring to the instructional process. (City and Elmore, 22 pag.)
What if we make a small shift in our role and resources to bring multiple representations to our practice?
…, it is the change in the knowledge and skill that the teachers bring to the practice, the type of content to which students gain access, and the role that students play in their own learning that determine what students will know and be able to do. (City and Elmore, 24 pag.)
These learners need doodling in order to focus more acutely on what’s being said, and they demonstrate better recall when they’re allowed to doodle than when they’re not. (Brown, 21 pag.)
Just make a mark and see where it takes you. (Reynolds, n. pag.)
One of the hallmarks of learning at Trinity School is Faculty/Staff Forum, our peer-to-peer professional development. Today, Kato Nims and I facilitated as session on math, mindset, and learning progressions.
Title: Math, Mindset, & Learning Progressions
Facilitators: Kato Nims and Jill Gough
Description: Does a learning progression empower and embolden the learn to locate where they are and ask target questions to make progress: Come collaborate with others to tackle a task or two using a learning progression as a self- and formative assessment tool to experience a student’s point of view.
Prerequisites: None. Bring a pencil or colored pen, your growth mindset, and a partner.
This activity helped me see solutions from multiple lenses. Even though the learning progressions were math-based, I can see the potential for using them in science…with some tweaking. When I present STEM challenges to my students I encourage them to use trial and error and to redesign and improve their work. I need to make learning progressions for the next challenge I present!
Connect – I know children need the language to more clearly express their needs in math. They also need to know what they can do instead of saying “I can’t” because they can do something! Extend – I came away with a better idea of how to quickly assess my students’ levels at the end of a lesson and that allowing time to work with a partner or in a group is very important to extending my students’ learning. Challenge – to continue to do the work of getting our learning progressions written and finding the time to collaborate as a team.
Connect: Kids need to know what their goals are, as do their teachers. Kids should be able to solve problems in multiple ways. Extend: Kids can have more than one learning progression that they’re working on at once. Challenge: Allowing the class to explain what progression they are on with me jumping in to help them. 🙂 Becoming comfortable adding these into the classroom daily. It’s been hard for me going from saying state standards for 10 years going to this, but I think this is actually more beneficial!
While I don’t teach math on a daily basis, I found this session beneficial because I had an opportunity to practice using learning progressions.
It was very valuable to actually experience a student’s perspective while going through a learning progression.