A few weeks ago, I got a text from Fawn Nguyen asking if she could visit my school site and teach math lessons in a few different grade levels.  She is now working for Amplify and no longer has regular opportunities to connect with kids and hone her practice of teaching mathematics.  It was a gift to have her visit MUS yesterday and teach four different grade levels.  She taught in 6th, 5th, Kindergarten, and a 2nd grade intervention group.

My day was full with so many takeaways.  Here are a few that stood out:

1. K can work for 60 minutes straight on an engaging tasks.  Fawn sat down with a Kindergarten class and played the game of Nim with them.  She adjusted the game to have 8 cubes which was much more accessible to younger children.  She engaged the class by introducing Nim on the rug and then sent the students off in partners to play the game while she circled around asking the students questions while they played.  Several times she brought the class back to the rug for a short 5 minute conversation and again sent them back to explore with a new prompt or focus.  It was great to see her send the message starting in Kindergarten that math is about making sense of problems and figuring things out. The kids figured out important qualities about the game, such as “3 is a bad number” and why they want to go first and take 2 cubes.  High level thinking is possible at Kindergarten when you create opportunities for it to happen.  
2. Struggle needs to be coached.  I was observing a 5th grade class work on a challenging task involving fisherman taking a number of fish.  90% of the class quickly engaged in the task with very little guidance or knowledge of what to do.  We promote and celebrate struggle in every subject at my school site and most students have a level of comfort engaging in a task when they don’t know what to do.  A few students did not engage at first.  I watched Mrs. N check in with one of the students and after a quick minute of coaching around the importance of of struggle this student felt safe and motivated to engage.  He stayed engaged for the remainder of the lesson. He just needed a reminder that he was supposed to be struggling and off he went. 
3. Problem solving is about what you do, when you don’t know what to do.  One of the teacher moves Fawn made during the 5th grade fisherman task was deciding when to pause the group work and give a nudge to get groups unstuck.  While walking around and interacting with the groups of 3 who were working on vertical white boards, she realized that many groups did not know what strategy to use to solve this problem.  She also noticed that one group started to use the strategy of working backwards.  She got the classes attention and talked about the importance of problem solving strategies to help solve challenging problems.  She then asked if any groups had a strategy they were trying and why the selected that strategy.  After the one group shared why they chose to work backwards as their strategy, Fawn released the groups to keep going.   The kids owned the learning but Fawn played a critical role in orchestrating the conversations and the learning. 
4. Thinking is engaging – Fawn played Catch-Up with a group of seven 2nd graders during their 30 minute pull out intervention.  Catch-Up is a basic addition game filled with thinking and strategy.  The kids were hooked.  My intervention over the years have shifted to be based on games, problem solving, and mindset.  The most significant data piece that this change has produced is the even the kids who are struggling the most with math, still love it and are engaged in learning it everyday. Math is really fun if you allow kids to own the learning and make sense of the math.  It can be a beautiful and creative subject if filled with rich problem solving tasks and games.  
5. Observing is powerful.  Thanks to Fawn visiting, I spent about 2 hours of my day just observing.  I observed what moves Fawn made.  I observed students working in groups.  Most importantly, my focus was on observing to see how the kids responded to what Fawn did or did not do as opposed to when teaching, observing with a lens on how to move their thinking and mathematics forward.  
6. A rich task that is has a low floor and high ceiling can be engaging at a range of grade levels.  I got to see Fawn use the same game of Catch-Up with a 2nd grade intervention group and with a whole class of 5th graders.  They were equally engaged in the thinking.  The game has opportunities for students to take it to different levels based upon their own thinking and readiness.  
7. This type of learning is really hard to understand when you have not experienced it.  At a recent event a well intentioned parent asked if the problem with our math teaching is that we “play” to much and don’t do enough “brute” learning.   I would argue the opposite is true.  We don’t “play” enough in math.  An untrained eye might walk in to one of Fawn’s lessons and see kids taking and playing while the teacher just walks around the room.  It looks very unguided and messy.  To a teacher trained to teach through inquiry and problem solving, a lot of purposeful magic is happening.  Students are talking about their strategies and thinking.  The teacher is purposely checking in with groups, checking for understanding, and determining what next step each group should take and what next step should the whole class take together.  She is driving the class to a learning goal, all the while the students are making sense of the math they are learning and enjoying it at the same time.  To shift to this type of teaching and learning, our teachers had to experience this pedagogy before they learned how to implement it in their classroom.  We had opportunities for our school board members to visit classrooms while we pointed out the moves that the teachers were making, why they were making them, and how the kids responded to those moves.  The significant jump in test scores over the next several years was the additional proof that a lot more than “play” was and still is happening. Although, if you ask one of the students, they might tell you that they are playing math, and that is 100% ok with me. 

Through the UCSB Math Project I have had the privilege of learning from Rachel Lambert about her work with redesigning math classrooms to make them more accessible for all students, particularly for students with disabilities.  She recently published her first book, Rethinking Disability and Mathematics; A UDL Math Classroom Guide for Grades K-8.  I feel it is a must read for classroom teachers, special educators, resource teachers, and school administrators.  

She takes a very simplistic approach to identifying the pinch points in a classroom, the places where a math class is too narrow for one or more students to access, and has the teacher consider how to open up those pinch points so that all students can have access to the learning.  A key takeaway from her book is that we are not simplifying the learning or lowering the rigor, rather we are opening things up and providing support.  She uses great real life and classroom examples to paint a picture for what this looks like in application.  

Another key takeaway is the value of using empathy interviews with students in the design process.  An empathy interview is a one-on-one conversation with the user of the classroom, the students who you are teaching.  Ask them what allows them to feel successful in math class and what challenges they have.  The amazing thing about kids is that they tell you their pinch points.  

I have been reading Rachel’s book as part of a book club with Abbey, Sheri, and Mandy who are other elementary educators, discussing two chapters every few weeks. One of our rich discussions today was around teacher beliefs and the trust they give their students.  In Rethinking Disability and Mathematics, Rachel highlights integrated general education classrooms and self contained special education classrooms where teachers are using problem solving strategies found in Peter Lijedahl’s Building Thinking Classrooms, Choral Counting, Counting Collections, and CGI (Cognitive Guided Instruction). All of these strategies ask the students to make sense of the problems, apply their own strategies, and communicate their thinking with others.  Unfortunately, teacher either does not trust their students will be able to do these things  or they do not have sufficient training and resources to implement this in their own teaching.  Rachel points out the magic that happens for all students in the classrooms where it does.   

Rachel paints a clear picture of what high quality math teaching and learning looks like and that it can work for all children.  So far, I am through chapter 8 and I can’t wait to see what else she highlights so that I can strive to make math learning fun, engaging, and meaningful for all students.  I can’t wait to find out where the pinch points are in my classroom and then play with ways that I can open them up and provide support for the students that need it.

Danielle, a 6th grade teacher at my school, recently shared this March, 2018 blog post from Robert Kaplinsky.  I feel his point and the embedded TED Talk from Conrad Wolfram are just as relevant 5 years later.  Unfortunately, very little in math education has changed since 2018 in regards to the amount of hand calculations we still are required to teach and assess.

https://robertkaplinsky.com/didnt-teach-calculator-can/

Key Takeaways From NCTM Los Angeles 2022

by Jeff Linder 

1. Where are all the teachers?  The last NCTM had 12,000 attendees.  This year there are only 2,000.  This is at a time when there is substantial monetary support for professional development.  Is it due to the shortage of substitute teachers?  
2. Peter Liljedahl says:
   •  that thinking is a precursor to learning. 
   • diversity is a strength in group thinking.
   • students listen to teachers’ actions, not their words.
   • one way to show students that we believe in them is to put them in random groups instead of teacher-selected groups. 
3. Jay Meadows from Exemplars reminds us to build curiosity in the math class.  
4. John Felling introduced me to many fun math games that promote both thinking, strategy, and skill practice.   My favorite was Who’s In Between. 
5. Graham Fletcher highlighted the importance of a balanced math program with application, conceptual understanding, and procedural fluency.  He presented a 3-Act task for the application, followed by a tool talk for the conceptual understanding, and ended with a task from Open Middle for procedural fluency. 
6. Jennifer Lempp presented on the Math Workshop model.  Her presentation confirmed that all the principles of math workshop are alive in MUS classrooms. 
7. Christine Franklin from the American Statistical Association shared some great resources for teaching statistical concepts, such as mean and variability.
8. Jo Boaler presented on the new California Math Framework.  
   • The Framework was scheduled to get approved in 2021 but due to pushback it will not be approved until at least 2023.  
   • The three main areas are big ideas, all students having access, and data literacy. 
   • Currently, only 16% of students are taking Calculus in California high schools.  This is an example of institutional racism that the framework is working to change. 
   • Traditionally, passing Calculus in high school has been a prerequisite to attend top universities.  Harvard no longer require calculus for admission.  “Specifically, calculus is neither a requirement nor a preference for admission to Harvard.”
   • Data science is now an accepted replacement algebra 2 courses.  
   • Groupitizing 10 dots, for example into 4+4+2, is a predictor of math achievement.   My takeaway is to do more dot card number talks at all grade levels!  
9.  I am grateful for the opportunity to learn from so many amazing educators.  NCTM puts on a great conference, maybe next year more teachers will take advantage of it. 

In November 2019, I attend my 3rd CANMEE lesson study training. “Lesson Study is a Japanese model of teacher-led research in which a triad of teachers work together to target an identified area for development in their students’ learning. Using existing evidence, participants collaboratively research, plan, teach and observe a series of lessons, using ongoing discussion, reflection and expert input to track and refine their interventions.” (Teacher Development Trust) In short, lesson study is a professional development model where teachers plan, teach, and reflect together around an identified goal or focus. The key piece is one or more shared classroom experiences teaching real kids.

In the United States, the typical professional development happens in a school cafeteria, office building, often associated with a county office of education, or in a hotel ballroom or convention center in the form of a conference. These professional developments are led by teachers or more often by former teachers that have been removed from the classroom for a number of years. I am one of those teachers that has not lived the life of an everyday teacher for 9 years. The critical piece that is missing from this professional development model is the students. I can sound convincing talking about the latest research and teaching strategies with colorful slides directed at the teachers. But does it really work with students?

Lesson study incorporates teacher learning and training with real students. Students who are not robots and do not always respond or behave in predictable ways. In November, I attended the lesson study conference with Fawn Nguyen, Melissa Wantz, and Margarita Mosqueda. Three AMAZING classroom teachers that are now in coaching roles. After spending 2 days learning about lesson study, we decided to give it a try. We reached out to two third grade teachers, Erika Padilla and Jaqueline Leal. We targeted Erika and Jaqueline because they were two teachers that we have a good relationship with and are open to trying out new ideas. The two teachers were willing to give up a few hours or their after school time to let us experiment with lesson study.

For Fawn, Melissa, Margarita, and myself, we wanted to know what was the big deal about lesson study? Is it doable in our current structure? Is it a better model for professional development?
We met in December to determine our learning goal, when the public lesson would take place, and logistics we needed to work through to pull this off. Last week, the team of 6 met to plan a 3rd grade lesson on elapsed time. We started with the districts adopted math curriculum and picked the lesson that fell on the day of the public lesson. We call it a public lesson because it a lesson that we all observe together, with one of us teaching. In addition, we could invite other teachers, parents, and administrators. With this being our first attempt, we stuck with the six of us.

Besides students meeting the publisher and Common Core learning goal of calculating elapsed time, our team wanted to focus in on students communicating their thinking. We read through and dissected the publisher lesson. It was a strong lesson but we wanted to ensure we connected more to students. We felt that the more the students could talk about elapsed time in their own lives, the more they would connect to the lesson and the more engaged they would be. With the learning goals in mind, the six of us modified the lesson to meet the needs of the students.

Today was the public lesson. We went into the process hoping Erika or Jacqueline would volunteer to teach it. Understandably, they deferred to me. It was a new process with a group of highly respected peers observing. The safe thing was to let someone else teach. The exciting part for me was that I got to teach the class that has by twin 9-year old boys. It was a fun crossover between my professional and family life.

Immediately following the lesson, the six of us met in an empty room to debrief. Besides getting to see my two boys as math learners, the reflection process was the highlight of my morning. Fawn played the role of the content expert. She focused her observations on the mathematics and the students’ strategies. Margarita focused on how our two focus emerging bilingual students responded to the instruction. Melissa, whose expertise is in Language Arts, provided an outside perspective and led as the facilitator. Erika and Jacqueline provided the perspective of the teachers that work with these kids and teach the mathematics curriculum on a daily basis. Their feedback and reflection was a gift, one of the most influential professional learning experiences I have had in years. I feel all six of us grew significantly as educators today.

We ended our time by reflecting on the lesson study process as a whole. We all agreed it provided an amazing professional growth opportunity because of the planning and reflecting around a common experience with real children. Some of our other takeaways:

It is so valuable to take your time early in the year to set up your classroom norms, routines, and learning community. I benefited today as the classroom teacher because of the work Erika put in to establish those norms, routines, and learning community.

Knowing and connecting with your students matters. Being an outside guest teacher left me without the student connection, without knowing the individual student’s strengths and needs, and without them having that connection with me.

Although we want right answers, wrong answers provide more opportunities for rich mathematical discussion and student learning.

Provide opportunities for students to share their thinking with each other and take the time to truly listen to their thinking without judgement.

Let the students own the math and the learning.

We asked Jacqueline and Erika about their perspective about lesson study as a model for professional development. They asked for more and offered to take on the role of the teacher next time. Margarita, Fawn, and Melissa will continue to explore lesson study as they are all content specialists in the same district.

I want to wrap up this post with a HUGE thank you to Erika, Jacqueline, Melissa, Margarita, and Fawn for the opportunity I had to learn from them and to grow as an educator. Their willingness to share their diverse experiences and expertise helped me grow as a classroom teacher and as a person that supports classroom teachers in the area of mathematics. There are so many reasons we can generate for why the Japanese lesson study model won’t work in the US. Everyone of those reasons is worth overcoming so that teachers can learn with their peers, in front of real students. Afterall, the students are why we are here.

In December, Dan Meyer asked during his keynote address at CMC North, “What’s Your Question?” He went on to highlight how math, science, and literacy all converge in the practice of critiquing reasoning. Given the rise of fake news and alternative facts we have a responsibility to educate children to be critical consumers of information and data.

Dan Meyer’s talk, along with insights from “playing” with the integration of science, math, literacy, and technology with my amazing colleagues Jennifer Wilson and Vanessa Scarlett, has lead me to my driving question, How do we teach data literacy through the context of science inquiry? From that, additional questions have surfaced. Can we completely remove data standards out of the math program and completely teach them in the context of science? Are there technology standards that support the work we are trying to do with data in science? Do the expectations of data literacy in NGSS and Common Core Math align? Do teachers have the content knowledge to effectively teach data literacy?

As we go down this road over the next several years, here are some of my initial thoughts and findings:
· The data standards in the mathematics standards are designed to be taught and developed in the mathematics classroom. The math standards at any specific grade level are not sufficient to get to the depth of science understanding and thinking that we are looking for. For example, bivariate data is placed in 8th grade so that students have the ability to calculate the equation of a line, slope, and have experience with coordinate grids. Students can and need to use a scatter plot to see patterns in bivariate data as early as third grade. Although calculating the line of best fit, slope, or equation for the line adds value and precision to the conversation, it does not warrant waiting until 8th grade. Our first hand experience with students validates this.
· The data standards are typically taught in the context of a math book and not involving real experiments and student generated data. We have observed what we have intrinsically known, data taught within context is much more accessible to all learners. “Because raw data as such have little meaning, a major practice of scientists is to organize and interpret data through tabulating, graphing, or statistical analysis. Such analysis can bring out the meaning of data—and their relevance—so that they may be used as evidence.” NGSS
· Some standards such as mean are not introduced until 6th grade due to the need for students to be able to divide using decimals. By utilizing technology (Google Sheets or Excel) students in 3rd grade can easily calculate the mean and have an understanding of what is being done, without having the mathematical skills to hand calculate it.

Keep in mind that we do not believe in teaching standards early because a student is high. We have spent a significant amount of time educating our teachers and parents about our philosophy of going deeper, not ahead. We believe the shifting of some of the data standards allows us to go deeper in our science understanding and depth of thinking and that these shifts do not undermine this philosophy.

Here is our first draft at creating a scope and sequence to teach data literacy in the context of hands-on science inquiry. We would love your feedback and suggestions.

K-6 Data Skills Progression Draft

My “friend” Fawn Nguyen just posted

7 Deadly Sins of Teaching [Maths]

http://fawnnguyen.com/7-deadly-sins-of-teaching-maths/

I feel they are worth sharing. The first 7 sins come directly from Fawn. I added an 8th, because 8 > 7.

Giving extra credit. I don’t care where you teach, how old your students are, what your zodiac sign is, you’re going to have at least one kid who’ll ask for extra-credit “work” at the eleventh hour of the grading period. Don’t do it. Say no and walk away because the tears might come streaming down his/her face and you have to ration the use of Kleenex. And you should be ashamed of yourself for giving students extra-credit points for bringing in copy papers, sticky notes, dry-erase markers, tissue boxes, doughnuts. Yes, you should send me some.

Giving timed multiplication drills. Maybe there’s a well-documented success story behind this madness that I’m not aware of, but to me, it perpetuates the myth of faster-is-smarter. This practice raises self-doubt and affirms the why-should-I-even-bother mindset.

Giving out the equation. That’s like giving away life’s secrets to someone who flies to Paris to have lunch. Meaning, they don’t need it, nor did they ask for it. Your students’ conversations, their conjectures, their models — are all at the heart of a math class. To give away the equation is to passively (and aggressively!) dismiss our students’ abilities to think for themselves. It’s okay to eventually give them the equation in due time, just don’t start with the equation. Imagine if I just gave my students the equations for slope and area of a circle.

Teaching from one source. No one source is that good. The creators of that source would be fools to not concede that point. It’s like eating out at the same restaurant or boasting that you can make chicken 50 different ways. No you can’t, and nobody cares. Let one or two sources be your structural outline, your mainstay, then supplement it with your favorite lessons or other teachers’ favorite lessons. Remember, any well-crafted lesson outside of the textbook that you can bring in is your gift to your students. Tell them that. And with our prolific #MTBoS, you cannot afford not to supplement.

Talking, talking, you’re still talking. I pretty much end every workshop with this reminder: The more you talk, the less your kids learn. I plan each lesson using this as my go-to guiding principle. Math is a highly social endeavor, so for the love of Ramanujan and Lovelace, please stop talking so much so your kids may talk! Every question you pose is an opportunity for your kiddos to ponder [quietly by oneself first] and share their thoughts with peers. Every question! If you fret that your kids don’t talk in class, then I wonder about two things, 1) Do students feel safe enough to talk in your class? and 2) Is the question you’re asking interesting/worthwhile/challenging to even bother? (I must have asked hundreds of lame, boring, worthless questions, but I’m not giving up. I practice and get better.)

Keeping up with the Joneses. That colleague whose hair and complexion are always perfect is just not as funny as you are. That teacher whose students all adore her probably owns a cat that wants to kill her. And that “amazing” teacher whom everyone talks about probably sucks at everything else in life! And he might be a compulsive hoarder of all things creepy! So, don’t mind them. We’re not here to compete with one another. We’re here to make mathematics rock for our kids. There is one you and 24 hours in a day. Make time for yourself, make time for your family. We all have s#@$&y days that rob us of our wits and sensibilities, but recognizing that and committing to having a better day tomorrow are worthy endeavors. Our students need us more than they care to admit.

Being an a%$hole. No one wants to learn from someone who’s mean and angry and bossy. When we try to establish authority in the classroom, we may inadvertently end up being perceived as this person. The meaner we get, the less students want to have anything to do with us, so the angrier we get. It’s a vicious cycle, and everyone is losing. We’re the adult in the room, charged with a magnificent duty to establish a learning culture, which will not happen if we don’t behave like an adult. Children are said to be resilient, but they are also impressionable, and their impressionable minds are vulnerable — vulnerable to criticism, to shame, to false praises.

Giving mixed messages. Live the expectations you have for your students. Everything you do sends a message to your students. Send the message that you love math. Show them how to be curious, how to make mistakes, and how to learn from your mistakes and from the mistakes of others. Show them your wondering by asking “what if” about a problem the class has solved but you find interesting enough to take it further. Show them how to listen to the thinking of their classmates and how to ask questions to help you better understand their thinking. Show them how to be excited when presented with a challenging problem that initially looks way to hard to solve.

In February, I facilitated a professional conversation with the UCSB Math Project Leadership cohort around the use of technology in the math classroom. My belief at the time was that technology was not valuable unless it allows me as a teacher, to do something better than I can already do without technology or provide access that was not previously available. With the help of the amazing workshops and presenters at NCSM, and presentations by Janet Hollister and Fawn Nguyen at UCSB my thinking has greatly changed.

Our students live in a digital world. They must be able to read, write, and think in that world. Our math classrooms must include blended learning opportunities. In my classroom, students engage in face-to-face problem solving with rich tasks, using real hands-on manipulatives, charting their thinking on paper, and presenting their thinking to classmates for constructive feedback. This is the norm. Although a few apps appear in my classroom, I do not teach in a blended classroom. I am not integrating technology; technology is just a guest visitor. Students need opportunities to read problems delivered on the computer, use virtual manipulatives, record their thinking on the computer, collaborate with their peers and receive feedback on the computer, and use technology to do the calculations.

My thinking has changed and my classroom needs to change. Doing these things digitally did not meet my previous belief about technology integration as I was already doing these things as well, using my old school environment. I now believe that students need to be able to operate in both the physical, face-to-face world and in the digital environments even if it is not “better”. Higher education, the job market, and our students demand it. I have changes to make and learning to do!

My next post – If you’re not doing a rich task, the platform (paper and/or digital) is not the issue.