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Sunday, January 31, 2016

ECET2: Cultivating Passion, Practice, and Contribution

Day two at ECET2 in San Diego for me focused on how we cultivate passion, practice, and contribution in our own work as educators, with colleagues, and in our students. There is so much we can do, and we have to collaborate to do it well.

Working backwards, the night ended with the amazing song, We Shall Overcome, led by Boston Public Schools music teacher, Jeremy Collier. When a better video is produced I'll replace the one below, but for now that will give you a wonderful snapshot of Jeremy's wonderful talent and the passion and heart in the room.

Before that Janine Campbell and Crystal Culp inspired us with stories of their educational journeys and their tremendous work with students. Again, I hope to add videos of these stories because they are stories that should not be missed. Earlier in the day Jaraux Washington gave a clever, targeted talk too where she utilized the story and characters from The Wiz to point us in the right direction when it comes to teaching every child well. I want to revisit all of these talks in the days to come and embed their wise, loving, and targeted messages into my work.

During the breakout sessions I had the chance to think and learn more about delivering a math program that meets standards and focuses on mindset in engaging, successful ways. A collaborative team of teachers from DC public schools shared their thoughtful approach to making this happen in their own school.

I also had the chance to learn about a powerful program in Tulsa, Oklahoma led by Dr. Anthony Marshall. The session titled Empowering African Young Men to Excel in Schools provided many activities and approaches to use as a way to cultivate passion, forward academic growth, and encourage contribution for all students. I captured many of Dr. Marshall's specific point on Twitter which I'll storify and add to this post later. I want to relook at his words as I think about how my colleagues and I can better support our students.

Wendy Sauer from the Gates Foundation "celebrated and elevated" all educators in her introductory talk at the start of the day. She prompted us to focus on our teacher leadership work, and then we reached out to share that work with each other through an informal exchange. I had the chance to meet a number of educators and learn about their wonderful work during that share. Colleague circles were another highlight of the day. We were introduced to our circle team on day one, and then during day two, we focused together on a problem of practice using a strategic approach. The team represented educators from throughout the country and multiple teaching roles. Together we shared our ideas and experience as we made progress on a specific problem. It was a powerful experience.

During breakfast, lunch, breaks, and in the evening, there was time to meet teachers from all over the country, walk to the beach, talk with colleagues by the fire looking out over the ocean, and share ideas. Specifically at lunch I had the chance to talk with Massachusetts' educators and benefactors who are invested in making our schools the best that they can be. Powerful ideas, programs, and questions were shared at the table. I want to think more about what we discussed and how I might learn more and contribute to solutions to the problems highlighted. 

I remain grateful to the Bill and Melinda Gates Education Foundation for reaching out to educators to provide this powerful experience, one that will continue to motivate me and so many in the days to come. I am also grateful that my school system was able to give me the time and support my attendance here and I look forward to sharing the ideas and practice I learned about with my colleagues there. 

Saturday, January 30, 2016

#ECET2: Research and Development and Intuition?

The work we are doing at #ecet2 is led by wonderful data and powerful research. This reminds me that it is critical that the work we do in schools is led by quality, timely research and development too. Boaler's book, Mathematical Mindsets, also reminds us of the value of intuition when she speaks of the work and research of Sebastian Thrun, CEO of Udacity, research professor at Stanford University, and inventor of self-driving cars (and so much more). In her book, she notes that Thrun talked about "the important role played by intuition in mathematics learning and problem solving, and of making sense of situations."

Too often in schools, a teacher's intuition and voice are dismissed by an interpretation of data by someone who is distant from the classroom or context of the teaching situation. This dismissal leads to frustration on behalf of the teacher and potentially less effort or positive impact with regard to students. While it's important that we stay attuned to the research and use the data in powerful ways, it is similarly important to regard an educator's intuition too because that educator knows his/her context, students, and craft.

Boaler goes on in her book to discuss how Thrun used intuition to solve a problem with robot design and then notes "Sebastian describes the process of working out a mathematical solution that made sense to him intuitively, then going back and proving it using mathematical methods." Further, Boaler states that he advises children to "never work with formulae or methods unless they make sense and to "just stop" if the methods don't make sense."

Hence, as I think of the ways that wonderful data and research are supporting what so many educators have been advocating for and know to be true with regard to "celebrating and elevating" the profession, I am cognizant of the important interplay between intuition and research and development that happens in every school setting, and perhaps in every professional setting. As we step forward making decisions about our students' learning, we need to access and apply research and data, work with intuition, and collaborate so that the end result of our work is the best that we can do.

#ECET2: Celebrate and Elevate!

In many ways, it used to be a lot easier writing a daily post at an education conference because there were so many broad categories of needed change with regard to our work as educators. Also in many ways the solutions were general and somewhat simplistic. A blogger and educator like me could attend a conference, write daily posts, and return with big ideas such as "We need more computers" or "Professional learning opportunities must improve" or "We have to make our work more student centered." But now, it seems like there is greater deep, targeted information out there about what it truly means to teach and learn well, and this is a direct result of the knowledge age we live in. Everyone essentially is a knowledge worker and almost everyone is navigating multiple knowledge points online and off every day in their personal and professional lives. Learning and teaching touches every industry and organization, not just schools. And that fact has resulted in lots of research, data, ideas, contribution, and discussion about what it means to teach and learn well.

This move from a broad lens on education to greater specificity means that we have to think more deeply and strategically about the messages we send and the work we do. We have to put greater effort into our collaboration inside and outside of school environments because this is a sophisticated time of educational change and one or two voices will not suffice. Good answers, efforts, and service will result from quality collaboration that represents all the voices of the learning/teaching team including students, families, educators, leaders, and community members.

This change is why we see organizations like the MacArthur Foundation making big shifts in vision and action with regard to education. In the 2010 MacArthur Foundation video they note these shifts:
  • education to learning
  • consumption to participation and production
  • institutions to networks
At #ECET2 one of yesterday's keynote speakers, Irvin Scott, inspired educators as he relayed the focus of the Bill and Melinda Gates Education Foundation's work with educators. Essentially the theme that "Nobody knows teaching like teachers." led the discuss as Scott relayed the focal points of the Foundation's work with educators:
  • Nurture trust among teachers.
  • Focus on each teacher's potential for growth.
  • Inspire the intellect and passion driving teachers' work.
  • Provide time for collaboration and learning.
  • Put teachers in the lead. 
  • Recognize teachers as talented professionals.
He went on to emphasize that it's time to "celebrate and elevate" the profession.

Nate Brown from the Gates Education Foundation shared the image below which provides a pathway for school communities that "celebrate and elevate" teachers:

So where does this take us as educators in the field?

As I begin to think about this, I know that we can put this research into place if we're cognizant of the work we need to do:
  • Advocate and contribute to the presence of the focal points and processes outlined above in the places where we teach and learn with the following questions:
    • How do we build collegial trust?
    • How do we support each other with regard to professional growth?
    • How can we discover, empower, and share intellect and passion as we collaborate around issues and efforts to teach all children well?
    • How can we advocate for needed time for planning and collaboration?
    • How do we advocate for and contribute to structures and support for the development of teacher leadership in our schools and organizations?
    • How do we "celebrate and elevate" each other as we recognize and treat teachers as professionals?
  • Work to create teaching/learning organizations that follow the pathway above by decreasing isolation, encouraging greater share of quality resources and practice, leading each other forward, and looking for more ways to celebrate and elevate the work we do day to day.
As we continue to rethink our profession and redesign our schools for better, deeper teaching and learning, we do need to rethink our roles, structure, routines, and content, and we have to do this as collaborative teams of students, families, educators, leaders, and community members. Within each of our contexts, we have to look deeply at what we're doing well and what we can do better. We have to stay on top of the research and share what we learn and know to be true, and we have to do this with the common vision of teaching every child well. 

It is so gratifying to be at #ECET2 and to hear that what we've thought all along as educators is true--we know what it takes to teach well, and together with the right support we can really empower, engage, and make a positive impact on the lives of the children we teach and serve every day. 

Friday, January 29, 2016

ECET2 and TLI Intersect: School Redesign Challenge

As part of the Teachers Leadership Initiative supported by NEA, NBPTC, MTA, CTQ, I am a member of the school redesign cohort. Though we've just started this group, I can tell you that it is a dynamic group of educational thinkers and practitioners. The first online meeting and assignments have my head spinning with ideas and challenges.

First, the cohort was introduced to videos below that discussed the history of school design and structure as well as thoughts for redesign.

Then we were asked to think about what school redesign means to you, and how you hope to make that happen in ways that significantly impact a child's experience of school.

Fortunately, the school system I work in has embraced many ideas and practices which are positively moving us in a direction of better and more targeted, dynamic service to children. The inclusion of Professional Learning Communities (PLC), ELA/Math Response to Intervention (RTI), shared teaching models, substantial technology resources, STEAM centers and projects, social competency goals and revitalized curricula, and more modern professional learning constructs such as our recent unconference are moving us in that direction.

I hope that we'll continue this path with greater attention to teacher voice and choice, differentiated learning spaces and furniture, greater freedom with regard to technology use and inclusion, more varied group structures, thoughtful attention to time, greater attention to purchasing patterns and protocols, and deeper interest and facilitation of field study experiences and relationships with outside education-related organizations.

Specifically with regard to my practice, I am centered on working with my grade-level colleagues to continue to develop and grow our shared teaching model with student engagement, learning, and overall success and happiness as the primary focus. Today as I engage with teachers from all over the country, we will consider the Gates Education Foundation research with regard to teacher leadership and developing optimal teaching/learning communities. The two charts below from Teacher2Teacher will serve as a focal point in the work we do. Teachers are welcome to join the Teacher2Teacher community via this link.

#ECET2 Conference Focus: Collect Ideas

One focus of every conference I attend is to collect ideas. So many of the good ideas I use in my classroom every day have come from my attendance at great conferences as well as my online and real time share. As a collector of ideas, it's important to be cognizant of the focal areas you're currently working towards as well as to leave some time for serendipity too--ideas and content you're not specifically focused on, but will serve you and your teaching/learning community well.

Consider supporting Ms. Jackson's Project
Last night at dinner we talked about a lot of ideas and experiences in education as well as our own stories. I was struck by the many ways that Audrey Jackson reaches out to support her students and create community. In fact, she's raising money right now on Kickstarter to fund a farm trip for her students. My own experience of visiting a farm as a young city girl impacted my learning and parenting considerably, so I delighted in thinking about how that experience will impact Ms. Jackson's students. This is the link should you want to contribute.
Digi-Block Reference
Audrey also introduced me to a new tool, digi-block, which I'd like to explore as well. It's possible that teachers in my system are currently using this Common Core-friendly manipulative so I'll reach out to find out when I return. It was also exciting to think about the fact that Audrey and many other State Teachers of the Year will be meeting with President Obama at the White House this spring. As our conversation continued, I realized once again that there are many organizations and opportunities for educators to get involved in today thanks to the terrific connections we're able to make beginning with Internet platforms such as Twitter, Edutopia, Teachers.Do, PBS Media, Teachers2Teachers, and so many more.

As I learn today, I'll focus on school redesign with a specific attention to shared teaching models, interdisciplinary teaching/learning modules, math education, and school structure and routines. As I continue my work with the NEA/MTA Teacher Leadership Initiative (TLI), I am part of the school redesign cohort. Yesterday we began that work with an online gathering. During the event, we focused on the attributes of knowledge workers, future of learning, and changing education paradigms. That work will dovetail well with today's conference work, and what's better is that one leader from the CTQ school redesign cohort, Lori Nazareno, will be at the conference so I'll have the chance to meet her in person. Other members of the cohort will also be here.

Finally I want to leave room for those powerful serendipitous moments when you are introduced to people and information that you never thought about or considered with depth before, but now turn out to be tremendously motivating and empowering.

With an open, ready mind and a desire to listen to, understand, and collaborate around the stories, needs, and efforts of educators throughout the country, I begin day two of the ECET2 journey. Onward.

Thursday, January 28, 2016

Mathematical Mindsets: What is a Mathematician?

The book, Mathematical Mindsets, is a rich, deep book, one that will take me awhile to read from cover to cover and one that will take even longer to sink into my practice in ways that matter. Though, by reflecting on essential points, I'm able to begin embedding these rich ideas into my teaching practice both in words and activities.

Boaler prompts us to think deeply about the characteristics and actions of real math teachers and mathematicians young and old, novice and professional with a number of lists, lists I'll return to as I design, adapt, and apply learning tasks and endeavors with my fifth grade students. The ideas below are directly culled from Boaler's book. I've written an oversimplification of her ideas, hence you should read her book, but these lists will get me started when it comes to embedding her rich research and ideas into my practice.

You are a Mathematician when. . 
  • You are comfortable being wrong.
  • You try out seemingly wild ideas.
  • You are open to different math teaching and learning experiences.
  • You play with ideas without judging them.
  • You are willing to go against traditional ideas.
  • You keep going even when the work or problem is difficult.
You Teach Math Well when you
  • "open up the task so there are multiple methods, pathways, and representations."
  • "include inquiry opportunities."
  • "Ask the problem before teaching the method."
  • "Add a visual component and ask students how they see the mathematics."
  • "Extend the task to make it lower floor and higher ceiling." (wide breadth and accessible to many)
  • "Ask students to convince and reason; be skeptical."
You engage students when. . .
  • "the task is challenging but accessible"
  • the task is seen as a puzzle.
  • includes visual thinking tasks that brings about understanding
  • students have a chance to develop their own way of seeing the problem and solution
  • the classroom environment allows students to be unafraid of making mistakes and proposing their own ideas
  • students respect each others' thinking
  • students use their own ideas
  • students collaborate
  • groups represent diverse skill, ability, perspectives
Positive math activities often include these steps:
  • posing a question
  • going from the real world to a math model
  • performing a calculation
  • returning from the model to the real world to see if the question was answered or problem solved. 

Mathematical Mindsets: Myths and Facts

Jo Boaler's book will have a great impact on my teaching in the days to come. As I read the first half of the book today, I was struck by idea after idea and fact after fact about how to improve my work with regard to teaching math well.

As I go forward I first want to dispel the myths, and teach the facts about learning math and learning in general. Below I wrote down a number of myths and facts highlighted in her book. The words in quotes, unless noted to another individual, are Boaler's words. This list is a beginning list to help me teach math better. In no way is it a complete look at what Boaler is saying in her book. You'll have to read Mathematical Mindsets: Unleashing Students' Potential Through Creative Math, Inspiring Messages and Innovative Teaching to discover that.

Myth: Only some can learn math.
Fact: Everyone can learn math  You have to believe in yourself.

Myth: Learning is fixed.
Fact: A growth mindset is necessary for optimal learning.

Myth: Repetition of same practice sets will build skill.
Fact: Too much of the same practice does not build skill, but worthy problem solving activities, projects, discussions, games, and puzzles do build skill as well as engagement.

Myth: Math is mostly about procedures, calculation, and rules.
Fact: Math is reasoning, creativity, connection making, interpretation, and different pathways.

Myth: You have to overhaul an entire system to improve math education.
Fact: "Relatively small changes in teaching and parenting can change students' mathematical pathways."

Myth: Telling students that they are smart is the best way to encourage deeper math learning.
Fact: Rather than statements such as "you are smart," parents and teachers need to encourage the action of learning math: tenacity, creativity, collaboration, making, and thinking.

Myth: Mistakes demonstrate problems in students' learning.
Fact: "Every time a student makes a mistake in math, they grow a synapse." - Dweck. "Mistakes cause your brain to spark and grow." "Imperfection, in fact, is great for creativity and entrepreneurship. When mistakes are encouraged, "incredible things happen."

Myth: Avoid confusion
Fact: Disequilibrium, as Piaget claimed, leads to greater learning by creating problems to solve as well as prompting creative, challenging work.

Myth: Math is a performance subject.
Fact: Instead math is a subject where one can "appreciate the beauty of mathematics. . .ask deep questions. . .explore the rich set of connections that make up the subject. . . learn about the applicability of the subject."

Myth: The study of math results in right or wrong.
Fact: Math is a subject "full of uncertainty" and multiple paths. "When you learn a new idea in mathematics, it is helpful to reinforce that idea, and the best way to do this is by using it in different ways."

Myth: Math is mostly memorizing.
Fact: Math solves important problems. ". . ..those that learned through strategies achieved "superior performance over those who memorized." "The more we emphasize memorization to students, the less willing they become to think about numbers and their relations and to use and develop number sense."

Myth: Non-examples will confuse students.
Fact: It's often best to match an example with a non-example for deep learning.

Myth: Only humans employ math.
Fact: Animals display sophisticated math such as the way a dolphin communicates or how a spider spins its web.

Myth: It's useless to explain my thinking in math.
Fact: "Explaining your work is what, in mathematics, we call reasoning, and reasoning is central to the discipline of mathematics." "The powerful thinkers are those who make connections, think logically, and use space, data, and numbers creatively."

Myth: Math is a solitary subject.
Fact: "Math is a very social subject, a proof comes about when mathematicians can convince other mathematicians of logical connections." "A lot of mathematics is produced through collaborations. . "

Myth: You don't need to learn or use much math after high school or college.
Fact: "Almost all new jobs in today's technological world involve working with massive data sets, asking questions of the data and reasoning about pathways."

Myth: The best mathematicians are fast with calculation and problem solving.
Fact: ". . .mathematicians, whom we could think of as the most capable math people, are often slow with math."  Math "can be taught in a way that values depth and not speed, that enhances brain connections and that engages many more students."

Myth: Even though many parents "hated mathematics in school. . .they still argue for traditional teaching because they think it has to be that way."
Fact: School math is often very distant from what real math is--real math is "a creative, visual, connected, and living subject." "Mathematics is at the center of thinking about how to spend the day, how many events and jobs can fit into the day, what size of space can be used to fit equipment or turn a car around, how likely events are to happen, knowing how tweets are amplified and how many people they reach."

Myth: It's best to start teaching what we think of as traditional math as early as possible.
Fact: "In Finland, one of the highest-scoring countries in the world on PISA tests, students do not learn formal mathematics methods until they are seven."

Myth: Puzzles are just for fun.
Fact: "When students see math as a broad landscape of unexplored puzzles in which they can wander around, asking questions and thinking about relationships, they understand that their role is thinking, sense making, and growing. When students see mathematics as a set of ideas and relationships and their roles as one of thinking about the ideas, and making sense of them, they have a mathematical mindset." "Successful math users search for patterns and relationships and think about connections."

Myth: There is one good way to calculate and solve problems.
Fact: "The low achievers did not know less, they just did not use numbers flexibly--probably because they had been set on the wrong pathway, from an early age, of trying to memorize methods and number facts instead of interacting with numbers flexibly."

Myth: Math is a passive subject.
Fact: "A mathematical mindset reflects an active approach to mathematics knowledge, in which students see their role as understanding and sense making."

Myth: Challenging math that produces anxiety teaches students to work harder.
Fact: Anxiety is associated with the blocking of working memory.

Myth: Scripted math programs are best.
Fact: "When teachers are designers, creating and adapting tasks, they are the most powerful teachers they can be. Any teacher can do this; it does not require special training. It involved knowing about the qualities of positive math tasks and approaching tasks with the mindset to improve them."

Myth: There's no room for intuition in math learning and thinking.
Fact: "When students are asked to think intuitively, many good things happen. First, they stop thinking narrowly about single methods and consider mathematics more broadly. Second, they realize they have to  use their own minds--thinking, sense making, and reasoning. They stop thinking their task is just to repeat methods, and they realize their task is to think about the appropriateness of different methods. And third. . .their brains become primed to learn new methods."

The ECET2 Adventure Begins

Thanks to the Bill and Melinda Gates Education Foundation, I have the chance to learn with educators from across the country this week at the ECET2 National Conference. Upon arrival I had the opportunity to talk with Paul Toner, former MTA President and current educational consultant, and Audrey Jackson, this year's Massachusetts' Teacher of the Year. Tomorrow the events begin in earnest and we literally will be learning, connecting, and collaborating from early morning until the evening both Friday and Saturday, and than another half day on Sunday.

This is a rare and privileged opportunity to develop my craft, learn from others, and share ideas from my practice and my school community. I must say I'm grateful to have this opportunity.

Wednesday, January 27, 2016

Fifth Grade Forward Movement

We're reading Out of My Mind as we prepare for Draper's visit.
Overall we had a great day in fifth grade today. During math we studied plane geometry with lots of drawing and word work. Later we'll use hands-on projects and problem solving to study plane geometry more. At the end of the day, I had the chance to peacefully watch the students play a great game of basketball--there's many wonderful basketball players in my class.

I'll spend the rest of the week at ECET2 Conference. I'm looking forward to the learning and new ideas that I'm sure will impact my teaching/learning journey to come.

As it stands now though, next week we'll meet the author,  +Jarrett J. Krosoczka and learn all about writing books.

We'll also make our own foot-long and decimeter-long rulers as we begin to review, study, and learn more about decimals, fractions, and percents. Students will continue to create their digital math story problems, and we'll continue reading Draper's book, Out of My Mind. 

Community building will continue to be a focus as we work together to keep the room clean and welcoming, and support one another as everyone learns and collaborates. As far as professional learning goes, there's a parent-student meeting, local union meeting, child study meeting, and a local teacher naturalists event. I plan to be back at #edchat after a two-week hiatus due to school and family events too. Further, my alma mater, The College of the Holy Cross, is hosting an educator event too. I'm looking forward to joining educators who have graduated from Holy Cross to discuss our roles as educators and how that connects to our experiences at Holy Cross which for me was a terrific opportunity. Finally our team will meet again to solidify plans for Character Day, write and send another newsletter, one that includes videos of our Rube Goldberg Theme Day and upcoming field study information, and discuss other upcoming learning/teaching events and plans.

The plans are set for next week, and now the mind is free to embrace the big ideas and teacher connections at ECET2. Onward.

Unconference Success

In my opinion, today's unconference was a successful professional development event. I liked the fact that the sessions were thirty minutes and we had the chance to choose discussions that were meaningful to us. I enjoyed listening to colleagues' ideas which spurred more ideas to try and perspectives to take. I hope we'll do this again.

Are You a Member of the Polygon Club?

Students design a character that is a member of the Polygon Club. Students complete a membership card for the character (see below). Students might want to design the club too. Characters can be designed online with any drawing tool. I used Google Draw. They could use animation tools or paper/pencil. This can make an engaging display in the school as one way to invite all students into the language and concepts of geometry. Let me know if you have ideas to add to this.  - Maureen Devlin
You need to have the right “properties” to join the Polygon Club. This is an exclusive club, not an inclusive club. Three dimensional solid figures, figures with curved lines, and lines alone are not invited.
  • Thank you, The Management: Sammy Square and Robie Rectangle

Polygon Club Rules
The Polygon Club is a special club open to shapes that have the following properties:
  • closed figures
  • straight sides
  • two-dimensional (2D), plane figures

All members are welcome to use the restaurant and pool.

Irregular polygons may use the irregular polygon park.

All quadrilaterals may use the quad playground.

Only those figures with two sets of parallel lines can use the parallelogram jacuzzi.

Only those with all equal sides and four ninety degree angles can use the square hot tub.

Only those with all equal sides can use the rhombi tennis courts.

Those with equal adjacent sides may participate on the kite crossfit course.

Only those with four ninety degree angles may play on the rectangular trampoline.

Only those with one, and only one, set of parallel sides may use the club’s trapezoid skyline room.

Polygons with more than four sides may use the hexagon and octagon fitness rooms.

Polygon Club Membership Card
List all of your polygon properties below:


Rooms that you have permission to enter include the following highlighted areas:
Polygon Restaurant
Polygon Pool
Irregular Polygon Park
Quad Playground
Polygon Video Room
parallelogram jacuzzi
Square Hot Tub
Rhombi Tennis Courts
Kite Crossfit Course
Rectangular Trampoline
Skyline Room
Fitness Rooms

System's First Unconference

This afternoon the elementary level of our school system will host their first unconference. A number of educators have signed up to lead conversations about topics that they're interested in sharing with others.

Teachers.Do is an open source platform open to all educators
I signed up to lead two discussions. The first will be about the new educator open source share platform, Teachers.Do. Teachers.Do is beginning to engage a number of educators with open content share and online discussion. I really like the way the platform  is emerging and believe it can help teachers to access terrific resources and advice when needed. During the conversation, I'll begin with the question, "What do you want to know or share about Teachers.Do?" I'll introduce the platform if people are interested, and I'm hoping the conversation will grow to include discussion about our use of online platforms with regard to teaching well.

The second conversation I'll lead is one related to the intersection of visual literacy and math education? We'll begin with the question, "How do you think math education and visual literacy intersect to positively promote student engagement, empowerment, and learning success? I created a website to host initial information and will share the link during the meeting.

Image: Brian Kennedy's "What is Visual Literacy?" Presentation
Of course it's always a bit daunting to try something new. What if no one comes? What if the conversation falls flat? Yet, if I don't try this I won't know. On the other hand, there's a good possibility that I'll learn a lot and our collective teaching/learning team will grow tighter and stronger. I work with dedicated and bright educators. I'm looking forward to a conversation about open resources and research related to teaching well. I want to know what they think about Teachers.Do and why they might get involved or not. I also want to know about the ways they focus on visual literacy with regard to math education--how do they maximize the use of that powerful sense?  Time will tell.

Update: Note that Teachers.Do actually closed down a few days ago. With the growth of dynamic resource sites like PBS, it was determined that the Teacher.Do effort would be integrated into Teacher2Teacher instead. Teacher2Teacher is currently a live teacher share site.

Engaging Flocabulary: Give it a Try!

I typically weave short videos throughout a lesson to provide students with introduction, repetition, or summary. Students look forward to singing along, dancing with, or simply just watching the videos. The videos provide an engaging way to review important vocabulary and concepts related to the daily learning focus.

When I say, "It's time for a video," the typical response is,

"Flocabulary Please!"

Students love the upbeat hip hop rap and song that Flocabulary offers. Important concepts are animated and include humor too. The clever rhymes give new voices to many concepts across all facets of the curriculum. The short animations include characters that represent many cultures and employ lots of models and explanation in their thinking.

In addition, Flocabulary's "Week in Review" is a great ice breaker when it comes to current event discussion and interest. These short introduction's to the world news are produced with two levels, one for the K through grades 4 or 5 crowd, and one for grades 5 to 12.

Take a look at Flocabulary's Digital Citizenship video below to try it out.

Right now you can sign on to Flocabulary for a free 75-day trial. I recommend!

Tuesday, January 26, 2016

Teacher as Researcher: Developing Practice by Reading Mathematical Mindsets

I picked up Jo Boaler's book, Mathematical Mindsets, and began reading. Right away I realized that this is a book that is going to forever impact the way I think about and teach math. I was struck with that sense of humility right away that says, You have a lot to learn!  

Reading books by educators who use brain knowledge and research to forward the way we teach is the way to go these days as we think about teaching and learning. These books have a lot to teach us as educators because so much of what we do day to day is rooted in practice and information that is not supported by brain study and knowledge. Systems and educators who understand this will not be satisfied with teaching and learning that is limiting or limited. Instead we will advocate for the time and support to learn more and implement that good learning in our daily practice and share.

As I think of Boaler's book, I realize that I am lucky to have the chance to work with children everyday so that I can readily impart this new learning and study into their daily learning. I will read the book with the overarching question, How will this book impact my teaching everyday so that all children learn in ways that are engaging and empowering?

I've invited my colleagues in my school system who are interested in discussing the book to join me on Monday, March 14th from 3:30 to 5:00 to discuss the book. I'll provide the refreshments. Then during the next week, +Rik Rowe and +David Hochheiser have kindly agreed to devote the #edchatma Twitter discussion on Tuesday, March 22 from 8pm to 9pm to a discussion about the book. The book's author, Jo Boaler, plans to join us for the chat so it should be terrific. All interested educators, family members, math enthusiasts, and students and of math education are welcome to participate in the chat that evening.

Monday, January 25, 2016

Collegiality and Changing School Structure

As elementary schools begin to take on new structures, roles, and routines, I am wondering how we meet those changes in ways that matter.

In many cases elementary schools have had a patriarchal or matriarchal structure with one or two leaders at the helm and many teachers who report to those leaders. This family-like structure, in a sense, is a top-down structure. Newer models of education are focusing on the positivity of shared or distributed leadership and teacher leadership. These new structures create the need for new ways to think about the way we meet, share ideas, and develop schools.

In some ways these changes at the elementary level may begin to mirror departments in high schools and college/university levels, and with that in mind, should elementary school teachers and leaders look to literature about successful collegiality at these levels with new models of teaching and learning in mind.

On the other hand, the way we are asking teachers to teach and students to learn at high school and the college/university level now mirrors, in some ways, the way school has often been taught at the elementary level with greater open, differentiated, multi-modal programs for learning that meet a child where he/she is. So while elementary school leaders and teachers may gain insight by looking at collegial models from high school and higher ed, higher ed and high school may gain insight by looking at how elementary schools teach students in more holistic, interdisciplinary ways.

In summary, to grow our schools, we have to look for models outside of our school levels and contexts--we need to look for those who have insights as to the roles we want to embrace and the ways we want to develop in order to do a better job as we teach children well.

Character Day

We may connect attributes to character with polyhedra study.
"I have a dream that my four little children will one day live in a nation where they will not be judged by the color of their skin, but by the content of their character." - Martin Luther King

On February 12th, Abraham Lincoln's birthday, our students will celebrate character day. During that day students will study the attributes of good character, a list culled from a web article.

It's difficult to develop good character if you don't know what good character or the "content of their character" means. Hence students and teachers will think deeply about the meaning of character.

Since it's Lincoln's birthday, I imagine that we might read books about Lincoln's life and discuss his character. It's also close to Valentine's Day and perhaps we'll create an activity that blends that special day and character. We'll also come up with a menu of creative activities that children can engage in to deepen their understanding of character. It's likely the list will leave space for students' creative ideas too.

Do you celebrate character day? If so, what do you do? In the days ahead we'll collect a number of ideas.

We hope to use the language and lessons from this day later in the year as students study Global Changemakers and think about the character of those famous people throughout the world who contributed to meaningful change and progress.

Productive Struggle: Volume

I handed each student a bags of 40 cubes and asked each students to create a rectangle prism using all the cubes. Students started building. There were many questions and lots of trial and error. Few realized that length times width times height equal volume. Most started building before thinking about the numbers involved.

It took the students a long time to build. The cubes were somewhat difficult to connect, but it was also clear that they haven't done this much. In time, however, we had many different rectangular prisms with volumes equal to 40 cubic units.

We discussed the project beginning first with naming the properties of a cube. That helped students to identify the important language and concepts involved. Students will revisit those concepts and words again later in the week when they build a number of solid figures from nets. Then students shared their creations as I drew a picture of each one on the board and listed the dimensions.

Tomorrow we'll use our POWerful SRSD problem solving approach to solve a multi-step volume problem. Later in the year we'll study volume with greater depth, but for now, these activities provide a good start.

Note: It is important to define prism for this problem. This information comes from Math is Fun

polyhedron is a solid with flat faces
(from Greek poly- meaning "many" and -edron meaning "face").
Each face is a polygon (a flat shape with straight sides).
So: no curved surfaces!

Examples of Polyhedra:

CubeTriangular PrismDodecahedron
Its faces are all squaresIts faces are triangles
and rectangles
What faces does it have?

Common Polyhedra

 Platonic Solids

Many More

Animated Polyhedron Models 
Explore 100s of Animated Polyhedron Models.
You can also see some Images of Polyhedra if you want.

Counting Faces, Vertices and Edges

When we count the number of faces (the flat surfaces), vertices (corner points), and edges of a polyhedron we discover an interesting thing:
The number of faces plus the number of vertices
minus the number of edges equals 2
This can be written neatly as a little equation:

F + V − E = 2

It is known as Euler's Formula (or the "Polyhedral Formula") and is very useful to make sure we have counted correctly!

Let's try some examples:

This cube has:
  • 6 Faces
  • 8 Vertices (corner points)
  • 12 Edges
F + V − E = 6 + 8 − 12 = 2

This prism has:
  • 5 Faces
  • 6 Vertices (corner points)
  • 9 Edges
F + V − E = 5 + 6 − 9 = 2
But there are cases where it does not work! Read Euler's Formula for more.

Details Catch Up to You

How many times have you let a little detail go only to find that it catches up with you. That's the story of school life. Every detail matters, and when you let a small detail go chances are it will snowball only to find you with a much bigger matter on your hands.

Today as we shored up a lot of routines and organization, it occurred to me that there were a number of details with respect to schedules, supplies, classroom/school protocols, and expectations that had snowballed a bit leaving us more disjointed than positive. Hence, through a number of activities we revisited the details. Some of the revisiting was targeted and graceful and others a bit too rushed, but nevertheless, we organized the team, routines, and learning so we can move forward with strength. Every so often a day like this is necessary.

Tomorrow as we embrace the learning in geometry and problem solving, we'll move forward with greater community and organization, and that will be a move in the right direction.

The Carrot

Image Reference
Over the weekend I reached out to an organization that I thought matched my son's strengths and interests well. I had heard about this match from one of my son's classmates' moms.

I filled out a form demonstrating interest, and the person in charge of the organization wrote a note to my son that included information about what my son might do to connect with organizations such as this one. My son was inspired by the short, seemingly generic letter. It spurred him on and gave him some vision as to what he wants to do and how he'll do it. In a sense it was a carrot for better work and deeper learning.

As parents and teachers we must always be mindful of the fact that we don't have all the answers and that it's important to reach out to make connections with others who may have what a child needs or desires. On the other hand, we need to be there to write that short note or lend a hand when we have what a child needs too. Together our potential to motivate and inspire students is amazing.