Math Talks are Awesome: Share Them!

So, I know I talk about math talks a lot, but there is good reason! They are such a versatile and accessible tool for promoting problem solving, discourse, precision, pattern-sniffing, and so much more.

As classes implement them more and more, they see the payoff in increase confidence and robust number sense. Many of my schools this year have asked me to help K-5 teachers get started using math/number talks in their classes, so I thought I would share my process for introducing them:

1. I start with a rationale for math talks, which is tailored to the school's perceived need (often this is building number sense in students, increasing engagement, and/or facilitating discourse). 
2. We experience 4 types of talks: Which One Doesn't Belong, Dot Talk, Number of the Day, and a computational number talk. I ask the participants to play the role of student and to suspend "teacher talk" until they have experienced the full routine. 
• Along the way, the participants have a template they use to jot down what they notice about teacher moves and students moves, any questions they want to ask after we experience the talks, and connections they see to the SMPs.
• After each talk we pause for them to think and ink, then we discuss noticings and wonderings they capture on their templates. 
3. Once we complete the first 3 types, I introduce the full protocol and do a number talk, stressing that this type comes after a safe classroom environment and community has been established. 
4. We pause for any additional noticings and wonderings and discuss, then they think-pair-share about these questions:
   - How might we use math talks to assist students in developing their understandings of the big
     ideas in our courses? How does this relate to number sense?
   - What are the big ideas in our courses that might lend themselves to math talks? 
5. I introduce my resource list and invite participants to play around with the sites on it.
6. Teams form to plan a math talk using this template. If there is time, I encourage them to practice with a partner or small group.
• Follow up is key, so either by passing that off to a leader or coming back, I make sure to have sharing of the one they tried in their classes at the next gathering. 

Here is a link to my slides: https://tinyurl.com/MathTalkIntroSlides

Here is a document where I am trying to compile websites that have "math talk-ish" prompts available: https://tinyurl.com/MathTalkResources

What am I missing? Please comment and let's make these working documents work for us.

Math Talk Progressions: Making Distributed Practice Meaningful

'Tis the season for anxiety around upcoming standardized tests. Woof.

Many of us feel that there is so much content over the course of a year that we may not have time to even get to every topic, let alone revisit it to practice or reinforce skills along the way.

Something I am noticing this year is that we, the adult math teachers, spend a lot of time thinking about scope and sequence and, if we are lucky, having vertical conversations to make sure the flow of our units and the big mathematical ideas makes sense over the course of our students' careers with us. But when do these messages get shared with our students? When do they get the opportunity to see the beauty of mathematics and how the big ideas evolve and connect?

NCTM's definition of procedural fluency points out an important truth:

Being in love with math and number talks as I am, I see a solid opportunity to merge some of the ideas I have been thinking about to build meaningful distributed practice. I wrote about my own progression of using math talks last April. As I have gone through this school year thinking about students' understanding of big ideas with teachers, purposeful series of math talks seem to be the answer to a lot of the areas students struggle to make sense of.

I think that sharing that overarching beauty of the big ideas would help them retain and connect and, therefore, remember the processes and procedures, too.  We can't accomplish this through isolated experiences.

Math Talk Progressions (#MathTalkProgs? Yes. Let's do this.) are series of related math talks that build toward an idea, representation, strategy, or understanding that we want students to take away. Inspiration can come from current learning topics, areas students are struggling with (i.e. fraction sense or place value), or just some fun topic you wouldn't otherwise make space for.

The Progression is meant to take place over the course of several days, and the goal is to illuminate patterns,

I designed this planning template, which has been helpful when first starting out designing these and still serves as a structured brainstorming place as I anticipate student moves and my questions.

Now, we have transitioned into jumping onto slides pretty quickly during the design phase of writing these. You can find some on my Math Talk Progressions page. I will continue to add as more are developed, and would love for you to contribute, too!

What other ways are you incorporating meaningful practice into your classes over time?

Navigating Numberless Word Problems

Do you struggle with students who have aversions to word problems? Do they just scan for numbers and perform any old operation on them without considering important context or relationships? Brian Bushart's blog is always an awesome read, but when I read about Numberless Word Problems last year, it was a total game changer for me in tackling this issue.

Numberless word problems are just what they sound like; word problems with the numbers (and question stems) removed, initially, to provide an opportunity for students to make sense of the relationships in the problem before rushing into computation. They are empowered to access the problem situation and employ their own wonderings, contexts, and questions to make sense of it. 

I have been working on NWP with some of the teachers I coach, and we have seen students ask lots of interesting and insightful questions about the situations presented, and many are even applying this idea of slowing down and working to understand what is happening in problems before rushing to compute.

Recently, we have been adapting questions from the standardized test they use to get at the structure of those items through NWP math talks. 

This is the general structure we use to plan (it can certainly be modified depending on the problem, like in this geometry example). We also brainstorm questions we anticipate students might come up with and choose one for a final slide where we actually ask them to solve.

Here is an example from a test prep resource:

So where can you find Numberless Word Problems to use with your students?

• Start with Brian Bushart's blog: https://bstockus.wordpress.com/numberless-word-problems/
• Develop them from existing problems found in your textbooks or other resources
• Write them based on real school or classroom scenarios (i.e. planning for a field trip)
• Get in on the Twitter action with #numberlesswp and share your amazing ideas!

Math Fun for a Crazy Week

It is so close I can taste it!

Here are some of my favorite math activities for those unexpected times when you have a group in front of you that you had not planned to see, or to see for that extra 20 minutes.

1. SolveMe Mobiles from EDC: https://solveme.edc.org/Mobiles.html
These puzzles are set up like the mobiles hanging above your infant's crib, and they present "multiple balanced collections of objects whose weights must be determined by the puzzler." They gradually increase in difficulty, and there is the option to build your own puzzles, too. Lots of algebraic reasoning going! They also have other amazing puzzles (my other faves are Mystery Number and Who-Am-I and a paper handout of some samples.

2. Central Park by Desmos: https://teacher.desmos.com/centralpark
Students move from guesses to algebraic rules to design parking lots that place barrier in the appropriate places. This is a great tool for transitioning students from arithmetic to algebra, and fosters the "Guess-Check-Generalize" thinking that helps them make that move.

3. Open Middle Problems: http://www.openmiddle.com/
Searchable by grade level and content strand, these have been my jam this semester, and kids absolutely love them. I have found that setting up some templates for them to use for the problems I have given them helps them understand the structure at first. This support can be gradually taken away as they get used to the way these amazing problems work.

4. Graphing Practice: http://www.math-aids.com/Graphing/Four_Quadrant_Graphing_Characters.html
Perhaps not as sexy as Desmos, but great for places with low or no tech. Put on some festive tunes and allow students to practice plotting points on the Coordinate Plane. The end result could be mittens, a present, or other holiday images.

5. Math = Love Activities: https://mathequalslove.blogspot.com/p/algebra-1.html
Sarah Carter is a super creative teacher, and generously shares her activities and ideas on her blog. Head on over to see her activities and you are sure to get inspired to try something new. Three of my favorites are Four Fours, Rolling Dice for Point-Slope Form, and Snowball Fight.

This time of year is definitely crazy, and I know that I am certainly looking forward to the opportunity to unplug and unwind. However, for many of our students, we should remember that breaks can bring uncertainty, changes in routine, and missing teachers, friends, heat and warm meals. So, in the midst of celebrating our impending, hard-earned break, keep in mind that some may not be looking forward to it and need some reassurance that we will be back soon better than ever.

Merry everything, and happy break!

Math Talk Feature: WODB

https://wodb.ca/ is brilliant.

I was enlightened to this resource's existence a little over a year ago via the magic of the #MTBoS. I have used it with students and teachers, both of whom love it as much as I do.

The biggest thing I have learned is that the prompt, "Which one doesn't belong?" was leading my students/participants to think there was one right answer, which I didn't want. Rather, I wanted to see what they knew about the numbers/shapes/graphs we were analyzing, and their relationships to each other.

So, the prompt shifted to "Find a reason why each one doesn't belong," and the reasoning and open communication followed; students began making observations and noticing things that I didn't even think of, because they were trying to find reasons for all of the quadrants rather than focusing on one "correct" answer.

The sample above is my favorite to use as a first experience with WODB for both teachers and middle school students. You can see the bullet points which are reasons 6th grade students shared for each number. My favorite is the second reason for 9: "only number whose digits don't add to 7." Awesome.

Beyond fun, this allows teachers to assess students' prior knowledge of numbers - vocabulary like perfect square, prime number, factor, multiple, and digit all came up naturally in this class.

One of the teachers I work with this year is developing many of his own with graphs and equations for an Algebra I class, and we are seeing students make sense of the features of both as well as the relationships among representations. We were inspired by images like these from the site:

I am excited about this resource, and hope we can all continue to contribute ideas to grow it more and more. I will leave you with some of my favorite shapes sets:

The Way We Say the Things We Say

I have been thinking a lot lately about language, and becoming more mindful of the way I phrase things during coaching visits and broader education conversations.

During a recent coaching visit, a teacher stopped me during our post-conference and said, "I just have to tell you, when you say 'our students' it makes me feel like you really care about us, and I get why my students are so comfortable with you." Aside from the warm fuzzies I felt from her generous words, I was hit with a realization: we all need a lot more "we," "our," and "us" in our lives.

Life is hard. People are fighting battles everyday; be it anxiety, lack of sleep, relationship issues, dealing with grief, or a myriad of other issues, many of which are battles we fight alone. We try to keep private our struggles to keep up with the pressures of "being ok".

In so many contexts, there is this focus on the individual, and I think it is because we are all working so hard with so little formal acknowledgement of what it takes to do all the things. This is especially true in my experiences in education, and I am finding that is a common challenge for many of us.

Often, in classrooms where management issues prevail, I pay attention to language and there is often a focus on "MY classroom" or "MY time." We've all been there. But I think that simple shifts in language can not only build more cohesive communities in our classrooms, but also get us back to our roots of teaching as teamwork and not a competition.

Life is tough enough. Let's bring joy and togetherness to the forefront of our work.

Building Community in Mathematics Class

The best way to build a math community is through doing mathematics together.

I'm sure we all remember the first day of school when we woke up excited and ripe with anticipation about how our year would play out, only to be hit with a day full of rules, syllabi, and boredom that didn't actually look like a typical school day at all.

So let's flip that switch and start the year with mathematics, modeling the classroom we want to have all year. Norms are not set and learned in a day; they are nurtured and develop through discussion throughout the entire course of the year. By starting the year with an accessible, engaging, mathematics task and reflecting on what went well and what could be improved, we set the tone for this conversation and mindfulness about how our classes function to continue throughout the year.

I like to use this form to help gather students' reflections on the day.

Lots of folks in Twitter-land have great activities to use that they have generously shared. Here are some of my favorites:

• Sara Van Der Werf's "100 Numbers to Get Students Talking" has been fun for me to use with both middle school students and adults in professional development sessions. Establishing what group work looks like is achieved through purposeful scaffolding and photographs that she describes in her blog post.
• Annie Forest uses "Me In Numbers" to share some information about herself while also giving students a chance to showcase their number sense by providing a bank of numbers for them to reasonably match to a statement. I love how she then gives the students a chance to make their own that she attempts that night. 
• Sarah Carter uses "Broken Circles" to help establish group norms and roles. I love that it is a little variation from the wordy, algebra-heavy problems I tend to use, giving another access point to engage more learners. (Sarah also shares her awesome posters for classroom set-up).
• I also love these two books, which have card sets with clues to help kids work together to solve a math riddle. Get It Together has lots of levels and categories of problems, and even has a sample on its site to whet your palette. United We Solve is similar, and has a sample in the preview at this link.
• Get started with your daily number sense routines right away! Number talks are my jam, and I love using WODB at the beginning of the year since they are so open-ended, but there are many, many more.

Regardless of the task, focus on access, engagement, and reflection built around mathematics!