Sharing the Learning (2019 NCTM Annual Meeting – San Diego)

It feels like a dream, but this time two weeks ago, I was sitting in the opening session of the NCTM Annual Meeting in San Diego listening to Gloria Ladson-Billings opening keynote. (I’ll add a link to the video of her talk once it’s posted on the NCTM website.)

It was a whirlwind of a conference. I got to see my friend and former co-worker Meredith, hang out with countless #MTBoS colleagues, and attend so many great sessions! By the time the conference was over, my heart and brain were full to bursting. To get a taste, check out this Twitter Moment I created to capture many of my tweets from the conference.

I also took copious notes throughout the many sessions I attended. I’m not going to bombard you with all of my notes, but I did want to share short summaries and key takeaways from all of the sessions. I know it’s not the same as being there, but I’m happy to share the learning and spark some ideas for those unable to attend.

Here goes!

The Decision-Making Protocol for Math Coaching: Apply High-Leverage Practices and Advocate Change

Presenters: Courtney Baker (George Mason University) and Melinda Knapp (Oregon State University-Cascades) See tweets from this talk here.

In this session, the presenters shared the Decision-Making Protocol for Mathematics Coaching (DPMPMC). “A primary goal of the DMPMC framework is to increase the intentionality of coaching interactions by supporting the user to simultaneously consider mathematics content, coaching and teaching practices, and professional relationship building.”

If you’d like to learn more, check out the site linked above and specifically check out the two articles they’ve written about this protocol. The first is “Coaches Engage with Principles to Actions” from the September 2018 issue of Teaching Children Mathematics. The second is “The Decision-Making Protocol for Mathematics Coaching: Addressing the Complexity of Coaching With Intentionality” and Reflection from the March 2019 issue of Mathematics Teacher Educator.

One Takeaway: I like the dual-pronged approach to coaching. Whether you follow the protocol or not, I appreciate the challenge of picking just ONE mathematics coaching practice and ONE mathematics teaching practice to focus the work. There’s always so much we can do, but if we try to do too much, we decrease the coherence and impact for the teacher being coached.

Using Lesson Study to Empower All Students

Presenters: Kyndall Brown (UCLA) and Susie Hakansson (Retired)

In this session, the presenters shared an initiative from the California Action Network for Mathematics Excellence and Equity (CANMEE) to develop and implement a model of lesson study that places an emphasis on equity. The rationale behind this work is twofold. First, they want to make lesson study an integral part of professional learning and continuous improvement. Second, they believe equity and social justice the most urgent goal and challenge for mathematics education. You can access their slides and other materials in this folder.

One Takeaway: I really like the idea of using four focal students as a lens throughout the lesson study. “If we are to focus on equity, who do we select so that we shift our practices to impact positively students’ participation and their increase in mathematical proficiency?” Not only do you interview the focal students, but you also develop a profile of each one that:

  • is asset-based,
  • includes students’ prior knowledge (cognitive and affective),
  • includes student understandings,
  • includes outside of class attributes,
  • identifies learning goals, and
  • avoids deficit thinking.

Lesson Study and How to Generate Buy-in that Will Inspire Instructional Shifts and Evolve Teachers

Presenter: Chase Orton (Independent Consultant) See tweets from this talk here.

While the previous session focused on changes to the lesson study process, Chase focused on steps he takes to build buy-in and set teachers up for brave professional growth before the process even begins. The first step is the passion profile. According to Chase, teaching is a practice of identity. If we are going to ask teachers to undertake the process of lesson study, teachers need to reflect on their own identity – specifically their passions and their why – as well as get to know the identities of the others who will undertake the lesson study journey with them.

The second step is defining the ideal classroom. “Let’s say you’re teaching or witnessing the best math lesson ever. What does it look like? Be really specific, looking at what the teacher is doing, what students are doing, and what the classroom energy feels like.” This step creates a powerful pivot to establish focus for the lesson study as participants develop their research question. How does your ideal compare to reality? What forces are restricting your ability to create your ideal math classroom?

One Takeaway: I appreciate the effort Chase takes to do the very important work of investing in the people who are going to invest their time and energy into lesson study. How often do teachers feel like something is being imposed on them rather than feel like they are being included and part of a team effort? How often do they get the chance to reflect on their own experiences and beliefs and help set the goals for the work ahead? Chase has written extensively on his blog about his work with lesson. If you’re interested in learning more, check out these posts.

Minimizing the Matthew Effect

Presenter: Sara Van Der Werf (Independent Consultant) See tweets from this talk here.

If you ever get the opportunity to see Sara Van Der Werf present, take it! She is one of the most passionate and committed educators I’ve ever met. This session was effectively her throwing down the gauntlet that teachers can and must lead the way to change structures so that all students are successful. According to Sara, if we wait on superintendents and administrators, it will never happen. The great thing is that even if you can’t see Sara in person, she does a phenomenal job of writing about her beliefs and advice on her blog. For example, in her session she evangelized Stand and Talks as one of the best things she ever did to get students talking to one another, and for those who couldn’t attend, you can read all about them in this blog post. Be sure to also check out her posts on how she uses name tents to build relationships with her students and her post on why she loves cell phones in math classrooms.

One Takeaway: Sara mentioned that using color coding doesn’t get nearly enough attention as it should. She introduced us to the #purposefulcolor hashtag and shared an example of how she’s using color more intentionally to support students. For example, when doing a Which One Doesn’t Belong? she puts each image on a different-color background. Now students can say, “The red one doesn’t belong because…” rather than having to generate clunky language such as, “The one in the upper left corner doesn’t belong because…”

Leveraging the Predictable Design of Instructional Routines to Elicit and Use Student Thinking

Presenter: Danielle Curran (Curriculum Associates) and Grace Kelemanik (Fostering Math Practices) See tweets from this talk here.

It’s masterful how Grace Kelemanik and Amy Lucenta weave intentional and powerful pedagogical moves into instructional routines so they’re baked in from the start. Just take a look at the key teaching moves in the Try-Discuss-Connect routine:

What’s powerful about these teaching moves – individual think time, turn and talk, and the four Rs – is that they were intentionally chosen and embedded into the routine because of their alignment with research about how best to support emergent bilingual students and students with learning disabilities.

One Takeaway: I love learning about new instructional routines, but I was especially pleased with stepping back and making explicit connections between instructional routines, in general, and the effective mathematics teaching practices from NCTM’s Principles to Actions.

The Hierarchy of Hexagons: An Example of Geometric Inquiry

Presenter: Christopher Danielson (Desmos) See tweets from this talk here.

By this point in the conference, my brain was already feeling a little full. I chose Christopher’s session primarily to do something fun – exploring hexagons. However, I had previously read about this work on his blog, so I also wanted to experience it firsthand to help me bring this kind of activity back to do with my teachers.

The session did not disappoint! Collectively a room full of educators attempted to name, classify, and sort hexagons in meaningful ways.

  • What does it mean to say a hexagon looks like a comet? What are the defining attributes of all hexagons that are comet-like?
  • What do you mean when you say a hexagon is boxy? How many right angles are you saying it should have?

One Takeaway: During the session, Christopher centered our work around the van Hiele model for geometric understanding.

I’ll be honest that I only first heard about this model a couple of years ago and found it extremely useful when developing a progression of units and lessons across our grade K-5 curriculum. Interestingly, my colleague Edmund Harriss took issue with the van Hiele levels and started a lengthy, but insightful, Twitter conversation around these levels and geometry instruction in general. If you have a chance, I recommend perusing the thread sometime. My takeaway from the conversation mirrors this reflection from Christopher: “Yup. Not hard and fast developmental rules, but useful structure for describing student thinking and for planning instruction.”

More Than Turn and Talk: Supporting Student Engagement in Each Other’s Ideas

Presenter: Megan Franke (UCLA) See tweets from this talk here.

This was a fascinating session where Megan Franke shared research about the role of student participation in student achievement. A surprising finding in the research is that there isn’t an “ideal” or consistent profile of student participation or teacher support that is best for all students. Rather, the important thing is that teachers create a space where all students are able to participate in ways that work for them. For example in a classroom where there are whole class discussions, turns and talks, and collaborative problem solving, students have varied opportunities to participate.

One Takeaway: According to the research, student achievement is impacted if the student gets at least one opportunity every class to explain all the way through their ideas. If teachers only lead whole class discussions, this is unlikely to happen for all students but rather a small handful of students. This gives me a goal for next school year to share this research with our coaches, administrators, and teachers so they can evaluate their current classroom structures and adjust as needed to create opportunities in math class for students to find space(s) to participate that work for them.

Rethinking Mathematics Education (and Mathematics) through Neurodiversity

Presenter: Rachel Lambert (UC-Santa Barbara), Edmund Harriss (University of Arkansas), and Dylan Lane (Independent Researcher)

In this session, Rachel Lambert challenges the medical/deficit model of disability.

Differences exist, according to Lambert, not as deficits, but as part of natural human diversity. She went on to share research about people with dyslexia and dyscalculia. The medical/deficit model emphasizes the challenges these disabilities pose, but research has shown that people with these disabilities also have a set of strengths. She then ceded the floor to Dylan Lane and Edmund Harris. Dylan grew up with dyscalculia while Edmund grew up with dyslexia. They each shared their story, which emphasized the power of leveraging strengths rather than fixating on deficits.

One Takeaway: Often we oversimplify kids, especially when we see them struggling. There’s a false deficit binary of being high or low at math, but it’s not that easy or simplistic to categorize children that way. We are all a combination of strengths and challenges. If we can see all of each other, we can get past deficit thinking. We need to complicate the way we think about our kids, but also how we think about learning mathematics. Math has to have more ways for students to develop and demonstrate understanding – more linguistic for some, more visual for others.

Collaborative Coaching: How Can We Learn as a Team?

Presenter: Nicora Placa (Hunter College) See tweets from this talk here.

In this session, Nicora Placa talked about the important role of collaborative coaching as a different type of learning opportunity that allows all members of a team to learn together and take risks. When selecting coaching strategies to use in collaborative coaching, Nicora looks for tools that focus on foregrounding student learning and student thinking. In this session, she shared the plan for how she uses clinical interviews during collaborative coaching:

  • Background reading / Book study
  • Watch videos of interviews
  • Select tasks and anticipate misconceptions
  • Practice interviews with each other
  • Conduct and record interviews in team meetings / PD
  • Analyze interviews
  • Summarize and share what we learned

She also gave us an opportunity to practice conducting an interview in trios. One person acted as a “student” working on a math task, one person acted as the interviewer, and the third person recorded what the “student” and interviewer said. Afterward we reflected on the kinds of questions asked and alternatives that could have been asked to elicit more student thinking.

One Takeaway: I appreciate that Nicora shared the challenges of listening to student thinking:

  • Listening only for the right answer or particular solution path
  • Thinking about next instructional move instead of listening
  • Assuming students are thinking the way you are thinking
  • Not listening for what students know
  • Not trying to make sense of what students are doing

The sample questions as well as list of questions to avoid were extremely helpful.

The Whole-School Agreement: Aligning Across and Within Grades to Build Student Success

Presenters: Sarah Bush (University of Central Florida), Karen Karp (John Hopkins University)

The Whole School Agreement process aligns models, language, and notation across and within grades to that students see the regularity and familiarity in a cohesive approach to teaching mathematics. The presenters encourage centering this work around their articles:

One Takeaway: I’m excited to use this framework and these resources to support coaches and campuses. I was familiar with these articles, but I’ve never used them to center the work of creating whole school agreements. The presenters shared resources in these handouts that can help with the work:

Coaching Toward Common Ground: Creating a Shared Vision and Growing Professionally as a Team

Presenters: Delise Andrews (Lincoln Public Schools) and Beth Kobett (Stevenson University)

The presenters took us through a sped up version of a process they use to help teams create a shared vision and find common ground. First, we worked together to illustrate a picture of the “ideal” math classroom. Then we used our pictures to list qualities of our ideal math classroom. The presenters then posed a question to us, “If this quality isn’t there, what’s the opposite of that?” This led us to develop opposites for each one of our statements. Then we drew lines between them to create a spectrum, because often we’re not at one or the other. Rather, we’re somewhere in the middle.

Next, everyone in the group got to put a mark on each line to show where they are in their practice. This is very eye opening because patterns emerge. Perhaps as a team we are all doing really well on Thing #1, but Thing #3 is an area where we struggle. This can help us develop goals.

After picking one thing to focus on, we went through another exercise called 20 Reasons Why. Basically we had to come up with 20 reasons why that thing is the way it is right now. This is more challenging than it looks! It’s easy to come up with the first 5 or 6 reasons, but getting to 20 requires thinking beyond the usual suspects. Finally, if we had time, we would have sorted our 20 reasons and talked through the reasons for our sorting. For example, we could have sorted them into categories, “Things I can control” and “Things I can’t control.”

One Takeaway: I liked the idea of reversing assumptions. According to the presenters, breakthrough ideas happen when we challenge our original ideas and even reverse our thinking. What if the opposite is true? For example, if our team’s original reason was, “We don’t have time to plan these kinds of lessons,” we could turn it on its head and said, “What if we did have the time? How would we plan differently?”

Another example would be, “Our students who are struggling with 5th grade math don’t know basic math facts.” If we reverse our assumption, we come up with, “What if our students who are struggling do know some basic math facts?” (What? They don’t know any? Oh, they do know some. Good. We have a place to start.)

The End

Whew! Just going through all that makes my brain feel full all over again. If you attended NCTM what were your big takeaways? If you didn’t attend, but read through my tweets, this post, or other tweets, what piqued your interest or resonated with you?

Trying Out Quizlet to Practice Deriving and Recalling Multiplication Facts

[Update – I’ve added a four more Quizlet study sets to my Multiplication Facts Practice folder. The three “Practice Doubling” study sets are designed to provide students practice doubling a number, a necessary skill to be able to efficiently use the Doubling Multiplication Fact Strategy The “Practice Halving” study set is designed to provide students practice halving a multiple of ten, a necessary skill to be able to efficiently use the Use-Ten Multiplication Fact Strategy.]

As a member of NCSM, I get a weekly email called the Marshall Memo that shares summaries of a variety of education-themed articles. What I like about the Marshall Memo is that I get exposed to articles I may never have encountered on my own. Even better, while many articles are on topics that aren’t math-specific, I’m still often able to able to make connections to my own work.

Take this recent article from The Reading Teacher, for example, called “More Than Just Word of the Day: Vocabulary Apps for English Learners.” I don’t have access to the full article, but in this summary, Marshall notes that the authors reviewed 53 free vocabulary-teaching apps for grades 3-8. Out of all these apps, Quizlet was the only app they endorsed. That piqued my interest!

It also connected to something I’ve been thinking a lot about lately, which is the strong research evidence that retrieval practice promotes learning:

“Retrieval practice” is a learning strategy where we focus on getting information out. Through the act of retrieval, or calling information to mind, our memory for that information is strengthened and forgetting is less likely to occur.”

https://www.retrievalpractice.org/

If you’re unfamiliar with the IES Practice Guides, they provide research-based recommendations on a variety of educational topics. In their guide Organizing Instruction and Study to Improve Student Learning, Recommendation 5b is Use quizzes to re-expose students to information. The level of research evidence for this recommendation is strong, according to the guide. It goes on to say,

“…quizzes or tests that require students to actively recall specific information (e.g., questions that use fill-in-the-blank or short-answer formats, as opposed to multiple-choice items) directly promote learning and help students remember information longer.”

IES Practice Guide, Organizing Instruction and Study to Improve Student Learning, page 21

This also brings to mind “Rachel,” a thought-provoking blog post from Michael Pershan that has had me thinking about the interrelationships between deriving and recalling facts.

Suppose a student has just derived 9 x 4. If they’re confident and successful, they might have an opportunity to share that solution with the class — I might ask them to share their solution, and they might have a moment where they ask themselves, “wait, what was 9 x 4 again?” This is recall practice. Or, maybe, they are working on a larger problem in which 9 x 4 is merely a step, and their later work calls on them to remember the product of 9 x 4. They derive it, and then turn back to the problem and ask themselves, “what was 9 x 4?” Or perhaps, while working on a large set of multiplication problems, a student derives 9 x 4 and is then asked to derive 90 x 4. They ask themselves: what is 9 x 4?

Rachel by Michael Pershan

All of this thinking got me inspired to give Quizlet a try for creating study sets that provide students practice both deriving and recalling multiplication facts. I organized my study sets around the thinking strategies shared in The Book of Facts: Multiplication, published by ORIGO Education.

“Research show that the most effective way for students to learn the basic facts is to arrange the facts into clusters. Each cluster is based on a thinking strategy that students use to help them learn all of the facts in that cluster.”

The Book of Facts: Multiplication, ORIGO Education

If you’re unfamiliar with these thinking strategies, ORIGO has kindly created a one-minute overview video of each one:

For each strategy I created three levels of study sets in Quizlet. Level 1 focuses on reinforcing the thinking strategy. As students practice the flashcards, they are presented a pictorial representation of the multiplication fact that reinforces the thinking strategy. For example, if students are solving 8 × 5, the reverse side of the flashcard shows the product as well as a visual that reinforces the idea that each fives fact is half of the related tens fact. In this case, the array model shows that 8 × 5 is half of 8 × 10.

Front
Back (Level 1)

Level 2 focuses on a verbal reminder of the related thinking strategy. The front of the card remains the same, but the back of the card includes a reminder of what students can think about to help them derive the fact. Here’s the back of the 8 × 5 card in Level 2:

Back (Level 2)

Finally, in Level 3, the focus is on recalling the multiplication facts. The back of the card does not include any reminders; it just shows the product. If students get stuck, the teacher can ask the student to recall the thinking strategy they’ve learned, otherwise students should focus on recalling the facts.

In addition to the strategy-focuses study sets, I’ve also included three study sets that practice a variety of multiplication facts when students are ready to focus on recalling across all of the facts. Version 1 focuses on the x0, x1, x2, x3, x4, and x5 facts. Version 2 includes a wide variety of all facts. Version 3 focuses on the x6, x7, x8, and x9 facts.

You can access all 21 study sets on Quizlet. If you’re not familiar with Quizlet, there is a free version and a paid version. I’d recommend starting with a free account. If you’re a teacher, be sure to indicate it when creating your account because teachers get extra features.

Some words of advice, Quizlet offers a wide variety of modes for practicing study sets.

I’ve noticed that many of these activities show the product and students are supposed to answer with the multiplication expression. If you want to start by presenting the multiplication fact to the students, all you have to do is click the Options button and then change “Answer with” to “Definition” instead of “Term.” I recommend doing this because generally we want students to recall the product not the multiplication expression.

In the Flashcards activity, I recommend turning on Shuffle. If students are at a point of focusing on recall rather than deriving each fact, then I also recommend turning on Play. This will make the flashcard automatically turn over after a few seconds. This prevents students from falling back on counting strategies.

In the Learn activity, I recommend going into the options and deselecting “Multiple choice questions.” For retrieval practice, research does not recommend multiple choice questions. Rather, the “Flashcards” and “Written questions” are preferable Question Types for this activity.

In the Test activity, I recommend only the “Written” and “True/False” question types. Again, in all of these activities, don’t forget to change the “Answer With” option from Term to Definition.

And finally, if your students are not familiar with the thinking strategies in these study sets, then they may be very confusing and unhelpful to students. In The Book of Facts series, ORIGO recommends four teaching stages:

  • Introduce the strategy – Hands-on materials, stories, discussion, and familiar visual aids to introduce the strategy or sub-strategy
  • Reinforce the strategy – This stage make links between concrete and symbolic representations of the facts being examined. Students also reflect on how the strategy or sub-strategy works and the numbers to which it applies.
  • Practice the strategy – This stage aims to develop accuracy and increase ‘speed’ of recall. In this stage, a range of different types of written and oral activities is used.
  • Extend the strategy (to greater numbers) – Students are encouraged to apply the strategy to numbers beyond the range of the basic number facts. The activities in this stage are designed to further strengthen students’ number sense, or “feel” for numbers.

The Quizlet study sets I created fall within the Practice stage. If you’d like to teach these strategies to your students, I do recommend checking out The Book of Facts: Multiplication because it provides several activities at each of the four stages for each strategy.

If you try out these study sets with your students, let me know how it goes! I’m excited to be able to share this resource for retrieval practice to the teachers in my district. If I hear feedback from them, I’ll be sure to let you all know how it goes.

I’m on a Podcast!

Recently I was honored to be a guest on my school district’s Teaching & Learning podcast. Here’s the blurb about the episode:

On this episode, we sit down with Elementary Math Curriculum Coordinator, Brian Bushart. Brian has led the direction of elementary math in Round Rock ISD for the last four years and his impact on teaching and learning for thousands of students continues to grow every day. In this interview, we talk about how ideas around math instruction have changed over the years, how “Sense-Making” and “Notice and Wonder” have helped students move beyond an over-reliance on memorization when it comes to understanding numbers, algorithms, and essentially how the world works. Be sure to scroll down to the notes below as Brian shared a treasure trove of resources for math teachers at all levels, parents of our students, and all of us who seek a better understanding.

After listening to podcasts for several years, it was a fun experience to be a guest on one. I appreciate Ryan Smith, our Executive Director of Teaching & Learning, inviting me to chat with him and share my passion for mathematics education. If you’d like to give the podcast a listen, you can subscribe in your favorite podcast app. Look for Round Rock ISD T&L Show. You can also stream the episode and find links to some of the resources mentioned in the episode on the show’s website.

While you’re at it, I highly recommend checking out the episode where Ryan interviews former Instructional Coach and current Curriculum Specialist Gina Picha about math anxiety.

The Path Ahead

Last spring I wrote about how over the past few years I’ve continually revised and refined the scope and sequence of elementary mathematics in grades K-5 in my school district. You can read those posts here:

The tl;dr version is that I concluded the series in May 2018 with these parting thoughts:

…what started as a blog series where I was planning to reflect on the changes I might make for next year has instead reaffirmed that the work I’ve done with my teachers over the past three years has resulted in six scope and sequences that make sense and don’t actually require much tweaking at all. I’m proud of what we’ve accomplished. Are they perfect? Probably not. But they appear to be working for our teachers and students, and at the end of the day that’s what matters.

Source

Fast forward to this post I wrote reeling from my experiences at the Math Perspectives Leadership Institute in late June:

There is a HUGE disconnect between what [Kathy Richardson’s] experience says students are ready to learn in grades K-2 and what our state standards expect students to learn in those grades. I’ve been trying to reconcile this disconnect ever since, and I can tell it’s not going to be easy… I’m very conflicted right now. I’ve got two very different trajectories in front of me… Kathy Richardson is all about insight and understanding. Students are not ready to see…until they are. “We’re not in control of student learning. All we can do is stimulate learning.” Our standards on the other hand are all about getting answers and going at a pace that is likely too fast for many of our students. We end up with classrooms where many students are just imitating procedures or saying words they do not really understand. How long before these students find themselves in intervention? We blame the students (and they likely blame themselves) and put the burden on teachers down the road to try to build the foundation because we never gave it the time it deserved.

Source

What a difference a month makes.

In May I was feeling proud and confident of the work I’d accomplished developing and revising our elementary scope and sequence documents. A month later I’m calling everything into question and having a crisis of conscience about whether the scope and sequences I’ve planned are actually creating some of the struggles I was trying to prevent.

Back in July I closed my post with no answers:

But how to provide that time? That’s the question I need to explore going forward. If you were hoping for any answers in this post, I don’t have them. Rather, if you have any advice or insights, I’d love to hear them, and if I learn anything interesting along the way, I’ll be sure to share on my blog.

Source

This big question of how to reconcile the pace of learning for our youngest students with the pace of the state standards has been on my mind for months. Throughout the fall semester, I had countless conversations with colleagues in and out of my district. These conversations culminated in my taking a stab at revising our scope and sequences in grades K and 1 as well as proposing a new instructional model in grades K and 1. (Ultimately I made revisions to the scope and sequence documents for grades K-4, but I’m going to focus on K and 1 in this post.)

I’ve been sharing, talking about, and revising these document with teachers, instructional coaches, and curriculum specialists in my district for a couple of months now, and I feel like they’re finally in a shape that I want to share them here so you can see where all of this thinking has taken me since I last wrote about this in July.

As a point of reference, here are the Kindergarten and 1st grade units for the 2018-19 school year.

Kindergarten 2018-19

1st Grade 2018-19

Our curriculum is now open to the public, so if you’re interested in visiting any of these units to see unit rationales, standards, lessons, etc., you can do that here.

Contrast that with these proposed units for the 2019-20 school year:

Proposed Kindergarten 2019-20

  • Fall Semester
    • Unit 1 – I Am a Mathematician! (21 days)
    • Unit 2 – Beginning Number Concepts (30 days)
    • Unit 3 – Sorting and Classifying (30 days)
  • Spring Semester
    • Unit 4 – The Concepts of More, Less, and the Same (30 days)
    • Unit 5 – Joining and Separating Quantities (30 days)
    • Unit 6 – Building Number Concepts (30 days)

Proposed 1st Grade 2019-20

  • Fall Semester
    • Unit 1 – I Am a Mathematician! (15 days)
    • Unit 2 – Adding and Subtracting (30 days)
    • Unit 3 – Exploring Shapes and Fair Shares (27 days)
    • Unit 4 – Understanding Money (10 days)
  • Spring Semester
    • Unit 5 – More Adding and Subtracting (20 days)
    • Unit 6 – Collecting and Analyzing Data (10 days)
    • Unit 7 – Introducing Unitizing (15 days)
    • Unit 8 – Exploring the Place Value System (24 days)

Here are some of the changes and my rationale for them:

  • In Kindergarten we drastically reduced the number of units. Instead of 10 units, we’re down to 6. On top of that, the first unit has shifted from counting concepts to “I Am a Mathematician!” What does that mean? Here are the notes I took to describe this unit:
    • Exploring manipulatives
    • Exploring patterns
    • Reading books about counting, shapes, and patterns
    • Setting norms and expectations for engaging in a community of mathematicians
    • Establishing routines
    • Getting to know students’ strengths and areas of growth
  • I made the names of the units more vague. Rather than stress teachers out that their students should be counting to 5, then 10, then 20 in lockstep, I’m providing space for students to engage in number concepts in general. Teachers can differentiate as needed so students who need to work within 5 can continue to do that while other students are exploring 8 or 12 or 14.
  • I made the units in Kindergarten longer to give students time to “live” in the landscape of these concepts. This goes hand-in-hand with the new instructional model I’m proposing based on the work of Kathy Richardson. Now a typical day will include a short opening activity that’s done together as a whole class. The bulk of math time will be spent in an explore time where students self-select activities that are variations on the core concept of the unit. During this explore time, the teacher’s primary role is to confer with students and continually nudge them along in their understanding. Each day there is a short lesson close to help students reflect on their learning. Here’s a link to a sample suggested unit plan to help teachers envision what a unit might look like in grades K and 1. (Note: If you encounter a link you can’t access in the document it’s likely due to copyright that we don’t control.)
  • In 1st grade I reduced the number of units focusing on addition and subtraction. Similar to number concepts in 1st grade, I want to give students an extended amount of time to “live” in these concepts.
  • In 1st grade I moved place value to the very end of the year. According to Kathy Richardson, unitizing and place value topics are challenging for 1st graders. However, I have to include them because our state standards require it. In order to reconcile this, I want to give students as much of the year as possible for their brains to develop so they are working with the most up-to-date hardware when they start learning these critical concepts. Putting it at the end of the year also creates more proximity to when students will continue learning about place value in 2nd grade. I’ve even added a 2-digit place value unit to our 2nd grade scope and sequence to create a bridge and continue the learning.
  • In 1st grade, I created a unit just on unitizing and followed that up with a unit on place value. Using activities from Kathy Richardson’s Developing Number Concepts series, students will spend three weeks making, naming, and describing groups of 4, groups of 5, groups of 6, and eventually groups of 10. Then they’ll spend almost five weeks extending this as they learn how our place value system is built on groups of 10.

The units are just the tip of the iceberg. The math block in our district is 80 minutes and broken up across three components:

  • Focus Instruction (50 minutes)
  • Numeracy (10 minutes) – This used to be named Computational Fluency but I’m re-branding it because the names imply different goals.
  • Spiral Review (20 minutes)

So when I revised the scope and sequence documents, I also revised the learning across all three components.

Draft Kindergarten At-A-Glance 2019-20

Draft 1st Grade At-A-Glance 2019-20

Things to point out:

  • I’ve settled on a few anchor instructional routines across all grade levels – number talks, choral counting, and counting collections. That’s not to say that teachers can’t use other routines – I encourage them to – but my goal is to ensure that these three powerful, versatile routines are in everyone’s toolbox.
  • Kindergarten only has 60 minutes of math instruction in the fall semester so they don’t start spiral review until the spring semester.
  • In 1st grade the numeracy topics are fairly consistent across the year – skip counting, subitizing, making 10, and developing strategies for adding and subtracting within 20. My hope is that the consistency of topics across the year paired with the anchor instructional routines will allow the numeracy work to feel more like an ongoing conversation across the year.
  • In 1st grade creating, solving, and representing addition and subtraction problems is a spiral review topic over and over again. I want to ensure students have lots and lots of opportunities to engage with problems involving joining, separating, and comparing quantities.

Parting Thoughts

Now that I’ve started to get a plan in place, I have a lot of work ahead of me to create all the associated unit documents. I’m also going to be working on gathering teachers who want to pilot these new units. I’m wary of just dumping them on our teachers because they’ve already put so much work into learning the old units, and there are some heavy instructional shifts that might need to be made to make these units work. Thankfully I don’t think it will be too hard to find volunteers. Teachers who’ve looked at these plans and talked about them with me or their instructional coach have been really excited for the changes, so much so that I have an entire Kindergarten team trying out one of the new units right now!

While there are still a lot of unknowns and a lot of work ahead to support teachers, I do feel like all of the reflecting, conversations, and attempts at making a new plan over the past six months have brought me to a place where I feel like I’m moving in a good direction that I’m happy to follow for the time being.

Here’s to the path ahead.

The Annotated Numberless Word Problem

I recently modeled a numberless word problem in a 4th grade classroom. A few weeks later, I got an email about how the teachers were attempting to create and use some of their own, but they were encountering a problem…writing their own problems was harder than they thought!

They reached out to me for support, and I thought I’d share with you what I shared with them in case it’s helpful to anyone else creating their own numberless word problems.

1. Start with a problem

First things first, start with the problem you want to transform into a numberless word problem. Here’s the problem I started with for this example:

I type the problem on a slide, either in Powerpoint or Google Slides. You can create your problem on chart paper or on strips of paper if you’re working with a small group. I’m partial to digital slides because of some other features you’ll see later in the post.

2. Work backward

From here I create a copy of this slide and remove some of the information. Usually I start by removing the question.

Next I copy this new slide and again decide what information to remove. In this case I decided to remove the entire last sentence. That sentence dramatically changes our understanding of the situation. If you look at the slide below you’ll see that we know the total number of kids eating ice cream and the number of kids eating chocolate ice cream.

The situation is very open right now. The rest of the kids could be eating a variety of different flavors – vanilla, strawberry, chocolate chip. When I reveal the sentence that the rest of the students are eating vanilla ice cream, there’s a nice element of surprise because you aren’t necessarily expecting that the kids are only eating just two different flavors.

My next step is to remove one of the numbers. In this case I’ll take away the number of children eating chocolate ice cream.

Finally, I’ll remove the number in the first sentence to get me to the beginning of this problem. This is the first text students will read.

I structure my slides to minimize changes. I don’t want to overwhelm the students by revealing too much all at once. I will add new sentence, but I avoid changing language that’s already on the slide, if possible. More often than not I’m only changing a word like “some” into a specific quantity. There are rare instances where I’ll have to adjust a sentence as new information is added, but I try not to do that. I want the sentence structure to stay the same so that when the numbers are added that’s the only real change.

You might have noticed that I don’t include pictures on the slides with the text. This is intentional. I used to include pictures, but a colleague shared how distracting the pictures were for her students. Students were looking for meaning in them when they were only there essentially as decoration, with the intent that they would support visualizing. However, the pictures ended up confusing her students rather than helping because the students kept trying to make connections between the pictures and text. Since then I’ve avoided pictures on the text slides unless the picture is absolutely necessary.

3. Plan purposeful questions

The first step was to work backward to plan out each slide so that information is slowly revealed on each slide. Now it’s time to plan the questions I’m going to ask the students at each step along the way. I have two primary goals that I strive for in my questioning:

  1. I want students to visualize what the story is about as it unfolds. If they’re not “seeing” it, then they’re likely not making much sense of it.
  2. I want students to make guesses and estimates about quantities in the story using what they know about the situation and the relationships provided. I want them reasoning all along the way so that by the time they get to answering the question they are holding themselves accountable if their answer doesn’t make sense.

So now I go back through the slides in the order they will be presented and add the questions I plan to ask along the way.

Slide 1

Ask for a volunteer to read the story.

What are you picturing in your mind?
What do we know so far?
How many kids could be eating ice cream?
How many kids could be eating chocolate ice cream? Why do you say that?

Have students draw a quick sketch of the story so far.

Slide 2

Ask for a volunteer to read the slide.

What do we know now that we didn’t know before?
What does this tell us about the number of kids eating chocolate ice cream?

When a new slide is presented, I always ask a question to get students to state the new information. I’ve also worded this as, “What changed? What do we know now that we didn’t know before?”

Slide 3

Ask for a volunteer to read the slide.

What do we know now that we didn’t know before?
How does this number compare to our guesses? Does it make sense?
Are all of the kids eating chocolate ice cream?
What could the other kids be doing?

Slide 4

Ask for a volunteer to read the slide.

What do we know now that we didn’t know before?
What does this tell us about the number of kids eating vanilla ice cream? How do you know?

Have students draw another quick sketch of the story so far.

What question(s) could we ask about this math story?

Slide 5

What is the question asking?

Do you have all the information you need to answer that question?

Let students work on solving the problem. Confer with students as they work to look for strategies you want to bring up with the whole class.

4. The beginning and the end

Something I’ve been doing for the past year with numberless word problems is bookending them with visuals to add a little more texture to the experience.

The beginning

The first thing I do is find a high quality image or two to show the students and have them chat about before we dive into reading any text. My go-to website for images is Pixabay.

I type in a word or phrase related to the story problem, like ice cream, and more often than not I hit the jackpot:

I look for a photo that I think will capture kids’ attention and activate their prior knowledge of the context. It allows students who may be less familiar with a situation to hear the relevant language, such as ice cream, chocolate, vanilla, and cone, before we dive into reading the text.

Here’s the picture I ultimately chose to engage students at the start of this problem, along with some notes of how I’d facilitate the opening discussion with the students.

Image Source: https://pixabay.com/en/ice-ice-cream-milk-ice-cream-waffle-2367072/

What do you notice? What do you wonder? Give students 20-30 seconds of think/write time. Then let students share 1 noticing and 1 wondering with a partner. Finally let students share a few of their noticings and wonderings with the entire class. You may choose to record these in a t-chart, but it is not necessary for this problem.

Tell the students that today they are going to read a mathematical story about ice cream.

When I paste the picture on a slide, I always go into the Notes section of the slide and paste the source of the picture(s), usually the URL where I found it. On Pixabay, more often than not the photos have licenses allowing reuse.  You can find the license information to the right of each photo. I know in the privacy of your own classroom it feels easy to get away with grabbing whatever picture you can find on Google Images, but it’s good habit to pull legal photos to avoid unforseen issues down the road. And with amazing sites like Pixabay and Wikimedia Commons available, there’s no reason not to at least start by looking for freely available photos.

The ending

I’ve been making it a habit to close each numberless word problem with a short video. This serves two goals:

  1. It further builds students’ knowledge of the situation discussed. In the case of the problem I shared in this post, it was about kids eating ice cream so I found a short video of a kid making ice cream. Even if you can only find longer videos, you don’t have to show the whole thing. You could just watch the first minute (or whichever section is most relevant or interesting).
  2. It serves as a pay off for all of the hard work students just did to make sense of and solve the problem.
Here’s a link to the video I included in this problem

I’m sure you can guess where I go to find videos. YouTube has such an endless supply of videos, that I haven’t yet encountered a situation where I couldn’t find a video worth sharing. Sometimes it’s the first video and sometimes it’s the tenth, but it’s always there waiting to be discovered.

Final thoughts

Now that you’ve seen me put together this numberless word problem in pieces, here’s your chance to see the finished product. This link will take you to the slideshow for the finished product.

In the Notes section on some of the slides, you’ll see references to students sketching in boxes. I created a recording sheet to try out when I modeled a different problem recently. If you want to check out the recording sheet, here’s the link. I don’t have a lot of experience using it yet so I don’t want to say more about it right now, but I do want to share in case it’s helpful.

If you have any questions, don’t hesitate to reach out in the comments or tweet me @bstockus. And if you create your own problem, please share it with us on Twitter using the #numberlesswp hashtag.

Origin Story

This summer I was invited to give an Ignite Talk at my school district’s Teaching & Learning SummeRR Camp.

SummeRR Camp

It’s a talk I’m proud of because in five minutes I was able to share why it’s so urgent to me that we ensure sense making is the focus of our work with students. Students deserve to develop positive relationships with what they’re learning now. It’s a disservice to assume they’ll learn to like it later. We never know what doors are closed to students because they learned to hate a subject or grow up thinking they’re not smart enough.

It’s the Great (Big) Pumpkin, Charlie Brown!

At this point it’s become an annual tradition that I make a batch of numberless word problems based on the results of the Safeway World Championship Pumpkin Weigh-Off. I’ve collected together the problems I’ve written based on the results from 2016, 2017, and now 2018 in this folder. [Update: Thanks to a request from my daughter, I’ve added some primary level pumpkin problems as well.]As with all the other files I share, you are welcome to edit them if you want to tweak them for your students. All you have to do is make a copy if you have a Google account or download the file in an editable format like Power Point. You will have full editing rights of your copy.

If you’re looking for some more mathematical inspiration as Halloween approaches, check out these three blog posts I wrote which include lots of photos and ideas for how to use them to spark mathematical conversations with your students.

Enjoy!