Tuesday, December 17, 2013

Tis the Season for Scripts

Time is our most valuable commodity. We often forget that in the push for creative lessons, there is much creativity to be found in efficiency. If we become creative leaves us more valuable time to invest in improving how we teach and how we learn.

After attending Jennie Magiera’s (Teaching like its 2999) Google Scripts session at IntegratED SF, I found myself realizing how many of the actions we do each and every day that could be automated in order to give us time to delve deeper into our passions.

As the district technology coach, I meet with teachers throughout the day. This poses a scheduling nightmare, with long email chains back and forth figuring out times that work for both parties. Therefore, I wanted to automate setting up meetings. My first attempt looked something like this: every time a person wanted to meet with me, I they filled out a form with three possible meetings times.  Then, I would email them back, add the event to my calendar and confirm with them.

As you can see, this was still taking a considerable amount of time even with some automation. So, inspired by Jennie’s session, I created a form, ran Andrew Stillman’s Formmule script on it to create a calendar merge as well as an automated email. I embedded the form into a Google Site with my calendar next to it, set to busy/free view. This way people would be able to look at my calendar to see when I was busy or free, and then fill out the form to set up an appointment with me. Additionally, I wanted the email to cc the principal of the school the teacher selected. However, I didn’t want them to have to type in the principal’s email. Therefore, I learned, through extensive YouTube video watching, how to perform a vLookup function nested in an array function so that it would work in the Google form spreadsheet (check out my how to video!)

Bottom line, it took me a while to automate, but now it works like a dream. My meetings are automatically added to my calendar. Principals are in better communication with their staff so they can follow up with people who have met with me on a variety of topics. Finally,  it is easier for those setting up the meetings because they simply choose a time they’d like to have.

Take a look at the following ideas that came to me as I extrapolated application of scripts in other areas of improving efficiency. Two great sites to check out for scripts are Jay Atwood’s and Andrew Stillman’s:

Administrators scheduling meetings with staff:

Taking this further, I thought about administrators and how they spend a needless amount of time bouncing emails back and forth with teachers to set up meetings. Why not use the format I just talked about for scheduling meetings with staff?

Administrators giving authentic feedback:

Another big issues for administrators is giving authentic and timely feedback to teachers. Many administrators drop by rooms and want a quick and seamless way to provide quality feedback. I worked with an administrator to create a simple form on Google forms linked with autocrat. She and I developed a quick certificate with call out fields that corresponded to the form. Autocrat is able to fill in the fields on the certificate based on the principal’s answers to the form. Then, there is a quick personalized email sent out via autocrat as well as a nifty PDF certificate, the spreadsheet contains the email template and links to certificates.

Signing up for multi use spaces

With many teachers at school sites and quite a few events, scheduling the use of multi use spaces at a campus can be daunting. Rather than good old paper and pencil, by using Formmule, we can do a calendar event merge. Couple that with a Google form where teachers or administrators fill out the date and time while cross checking with the space calendar, and you now have an automated way to take care of scheduling. Formmule will add the event to a shared calendar for that space as well as email the person in charge of managing that space that someone has requested to use it.

Professional Development Choices

Running a professional development session? Need to limit the number of people who can sign up for certain choices? Try using Formranger and a simple script that will allow you to close choices on a form when enough people have signed up.

Document Ownership and Organization

Have kids who accidentally delete items or forget to share them with you? Check out Doctopus which is a virtual copier that allows you to choose who get a copy of a document while keeping you as the owner.

Doctopus add on for inserting rubrics and grading work--Goobric

Working with Doctopus is fun and exciting, but grading is also an important aspect that would be great to add onto this. Goobric works seamlessly with Doctopus as a way to insert a pre-made spreadsheet rubric into a Google Doc.

Grading a form with conditional formatting

Fubaroo is a quick way to grade multiple choice google forms, but another nifty way to grade them as well is with conditional formating. Check out Jennie Magiera’s YouTube video on grading forms with simple color rules.

Monday, December 9, 2013

LASD Joins Hour of Code

This week (December 9th-13th) is Computer Science Education Week, a week dedicated to showing students K-12 the importance of computer science education.  Organized by code.org with the goal to get 10 million students of all ages (and adults) to participate in the hour of code.  

According to code.org, "90% of K-12 schools in the U.S. do not teach computer science."  Los Altos School District, thanks to funding from LAEF, is fortunate enough to be in the 10% of U.S. Schools that are offering every student the opportunity to learn computational thinking through the STEM and CSTEM program.

During this week every LASD student will be given opportunities to engage in activities that will teach them to code.  A big thank you to all of our teachers that are making “Hour of Code” a reality across the district.

Here are a few sample lessons/activities being planned across our district this week

This week would be a great time to ask your child about what they have learned.  Perhaps you can help stretch the “Hour of Code” by engaging in some coding fun as a family.

To learn more about the the LASD STEM program, take a look at two articles written and published just this week by Sheena Vaidyanathan, CSTEM Teacher:
"Everybody in this country should learn how to program a computer…because it teaches you how to think."- Steve Jobs

Contributed by: Alyssa Gallagher, Director of Strategic Initiatives & Community Partnerships

Friday, November 22, 2013

Getting Lost in the Weeds

We live and work in a rapidly changing and fast paced environment. Everyday is a flurry of emails, text messages, traffic, technology challenges, and panic attacks as we wonder how we’re going to fit it all in. It’s easy to lose direction and find yourself off wandering in the weeds. I’ve spent a bit of time there lately and I’m thinking that it may be more than time wasted, sometimes, there’s bits of treasure to be found there.

I consider myself to be a bit short sighted at times. I love the thrill and rush of jumping into something new, the excitement that is generated as you travel down an unknown path,and the challenge of making creative ideas work. It’s how I run my classroom and why my students are usually engaged. I am never satisfied with the first implementation of an assignment or project as there are always ways to improve and elevate the experience. I am continually rethinking, reframing, and starting over because I need the adrenaline rush of creating and pushing further. However, this is an exhausting cycle and difficult to maintain. I sometimes lack good follow through and overwhelm my students by the sheer pace and constant change in my classroom. I can get so caught up in creating, that I lose sight of the trail and find myself wandering with little direction, my students wandering right behind me. When this happens, I am learning to stop. I believe that when you’re out hiking a trail, and you suddenly find yourself lost, you are supposed to sit in one place and wait for rescue. Although rescue in this instance, comes from clarity.

When I’m out there sitting in the weeds, my brain has time to process and pieces that weren’t fitting, are suddenly finding their place and the trail emerges. Some of the most interesting and valuable classroom conversations evolve from these moments. One wise ten-year-old once said, “Mrs. T, if you could just give us a little more time, I’m sure we could find a better answer.” Ah, time, the most sought after commodity by everyone.

Working as a district coach, I’m seeing the same issues on a larger scale throughout districts and education in general. We introduce cutting edge initiatives and programs, hoping to push new thinking and create updated learning experiences for our students. The work is exciting and the landscape is constantly changing. We have “wow” moments and we leap into the next innovation, hoping to build on each success. Most teachers are willing participants, who are excited to engage and are happy to get caught up in the journey, however, many become overwhelmed and lost due to the rapid pace and continual uphill march. It’s difficult to sustain without well thought out support and follow through.

We need time in the weeds. It’s okay to wander from the path at times because we often find better solutions and perhaps even a better direction. The important piece is recognizing when you’re there and knowing that you need to sit down. Find the time to define needs, process, reassess, think it through. Clarity will often reveal a new path that’s easier for others to see.

Contributed by Kami Thordarson, Innovative Strategies Coach

Monday, November 18, 2013

LASD Partners with zSpace

Every year in LASD is filled with exciting learning opportunities, but this year there are more than ever! During the past four months, we have been building out a new STEM (Science, Technology, Engineering & Math) program at all of the elementary schools. Thus far the focus has been on creating STEM opportunities outside of the classroom such as lunch clubs, supporting the physical science strand and creating a new computational thinking/computer science strand for students beginning in kindergarten.  While those are the areas most visible at the school sites, the STEM team has also been working behind the scenes to develop a new robotics unit for grade 4 with Khan Academy and to explore possibilities that will enhance the learning for students in STEM.  While we are constantly seeking out innovative opportunities for LASD students, we are clear that these innovations must help produce better learning outcomes. Our exploration has led us to develop a fantastic new partnership with zSpace.  

Just over two years ago, we forged a relationship with zSpace, at the time a small company who had developed an immersive & interactive holographic platform that had many possibilities to make learning more interactive for students.  While we were blown away with the technology and explored the possibility of partnering in some way, we determined it wasn't the right time.  Fast forward two years to now and we have once again engaged in conversations with the team at zSpace.  There have been several interesting developments both within zSpace and LASD that make it the right time to move forward with a partnership.  zSpace has a new focus on education and we have built out a STEM program creating the perfect space to pilot their technology.  Explaining zSpace is challenging, so I encourage you to check out their website and watch the short video on their homepage to get a glimpse into what might be possible.

Through our partnership with zSpace, we will help to develop and expand STEM learning tools in Earth, space, physical and life sciences for students in third through eighth grade.  Fifth grade students at Covington and Santa Rita Schools will be the first to implement the zSapce STEM stations through a virtual hands-on lab on the circulatory system.  Covington and Santa Rita will be joined by Springer and Gardner Bullis Elementary schools as well as Egan and Blach Junior High Schools before the school year ends in June 2014.  Should the first two phases of our pilot be successful, we plan to engage all nine LASD schools in phase three beginning Fall 2014. 

We will be hosting an open houses on Monday, December 9 from 5 - 7 pm in the Covington STEM lab and encourage you to come experience zSpace.  Experiencing zSpace will allow you to better envision how we will use it with students to enhance and extend their learning. 

Our STEM team continues to meet weekly to ensure we are building the very best program built on best practices, current research and the cross cutting concepts articulated in the Next Gen Science Standards.   The LASD STEM team is currently attending the first statewide STEM conference in Sacramento, where two team members are presenting are robotics and CSTEM. The development of a STEM program wouldn't be possible without the incredible support of our parents and the Los Altos Educational Foundation.  Thank you!  It is an exciting year of learning for all involved, but most importantly for our students!

Contributed by Alyssa Gallagher, Director of Strategic Initiatives & Community Partnerships

Friday, November 15, 2013

Spark, Whimsy -- the importance of learning simply to learn

Space Models at Brick Fest, Flickr via Creative Commons
Young children are encouraged to be whimsical and imaginative and to always ask why. Students in younger grades look with awe upon the lifecycle of a butterfly and draw endless pictures of colorful circles that they truly believe resemble their parents.
Then a few years pass. Times tables are memorized and we increase the content we teach and begin to instill a sense of conformity and pressure in our students that focuses on attaining success measured by society. It is no surprise that the imagination of our students changes to reflect a stale, stagnant state because they are learning what others want them to learn. Yet, our students are still creative underneath a shell of academic standards. However, we don't give them the opportunities to show the whimsical, inquisitive nature deep within them.

As teachers, we suffer from much the same ill-fated trajectory our students do. Believing we can change the world as a young teacher, we come to the first year of our teaching careers with an energy that feeds into our innovative lessons. Years pass and we are met with more strict standards, more programs to teach, less time to teach them, and more students, many of whom are bored and unengaged with the curriculum since they are being told what to learn and how to learn it.

Think of topics that you find interesting. Think of what you'd want to learn in school. Now think of what you teach. Think of how you teach it. Ask yourself, would I want to learn that way? Would I want to spend my afternoons at home doing that? A recent article came out about a revolutionary way of learning that focuses on engaging students with what they are interested in. Joshua Davis writes for Wired, "How a radical new teaching method could unleash a generation of geniuses." In it he explores a variety of progressive philosophies on learning.

Peter Gray, research professor at Boston college, is quoted by Joshua Davis as stating, " 'We’re teaching the child that his questions don’t matter, that what matters are the questions of the curriculum. That’s just not the way natural selection designed us to learn. It designed us to solve problems and figure things out that are part of our real lives, ' " which raises some key issues of institutionalized schooling. The whole purpose of school should be to teach kids a love of learning, a desire to understand the unknown, and the ability to apply what they know to questions they have. Ultimately its about the spark that fires up their curiosity thus raising their engagement in the classroom. It should not be about what other people think they need to know.

So, what if homework was filled with activities that truly sparked the curiosity of our children, thus supporting that their questions matter. What if students rushed to school the next day asking why, why, why? What if students eagerly awaited the next lesson rather than day dreaming through it?

A simple task like watching a video about space could be that spark for a child. A spark that could change the trajectory of a student's life, assisting them in realizing dreams they have. Take a look at these amazing videos on the International Space Station by Canadian astronaut Chris Hadfield.

Here are two class work or homework documents I’ve put together, one for primary grades and one for upper grades.

Take on the challenge of giving assignments that you’d want to spend time on. If you wouldn’t want to do it, why would your kids?

Inspired and want more? Additional resources can be found at Ramsey Musallam’s Cycles of Learning blog that discusses in depth the use of video as a curiosity spark for initializing a love for learning.

Thursday, November 14, 2013

Creating Space before Creating Change: A Cautionary Tale

I recently had the opportunity to visit a few schools that are creating amazing learning environments for students. Whiteboard walls, whiteboard tables, movable and adjustable furniture that can be reconfigured in a moments notice. Learning spaces that adapt to students’ and teachers’ needs, often with 1:1 technology available. Here’s what I observed: students sitting, isolated by headphones, focused on screens, furniture in traditional classroom layouts, blank white boards.

Now, I know that these room conversions were an expensive investment. I’m sure much thought went into which furniture to order, mac books or chromebooks, furniture and wall paint colors. I think these improvements to our school environments are not only wonderful, but absolutely necessary. However, I’m wondering if we are putting our early investment into the wrong place. If we don’t invest in the learning behaviors that happen within the space, what have we really changed?

It feels as if we are setting the stage without really understanding the script that will be performed. We bombard teachers with words and phrases: blended learning, project-based learning, design thinking, and then we create these wonderful environments which we release them into and say, “There, go do it!” Now, I know there are some amazing things happening in these spaces as well, early adopters who seem to naturally adapt and can clearly see the vision of new possibilities, but overall, the traditional roles of teacher, student, and school are hard to crack.

What I’m learning through my current journey, is that teachers want to change, students want new experiences, and most school districts see the need to do something different. I’m also learning that you can’t offer traditional professional development experiences, read a book, or attend a traditional conference and expect everyone to just walk away and “get it.” Most importantly, you can’t just order new furniture and paint the walls, expecting that everyone will just know how to perform in that new space.
The Classroom is Obsolete

Like anything that’s worthwhile, it’s a process that requires time and patience. Professional development opportunities need to model the instruction that you would like to see happening. Teachers need time for collaboration and sharing as they wade into new waters along with permission to take risks and make mistakes. It's important to create meaningful learning experiences for teachers outside of their classrooms until everyone experiences their "a-ha" moment. District leaders need to clearly communicate with parents regarding changing practices so they are able to support rather than question new classroom strategies. Schools need to build and define a new learning culture for students with updated expectations and establish new student norms. What does learning look like in that fancy new room? In any classroom? What does learning look like in today’s world? Can everyone see and define the same vision?

The famous movie quote, “If you build it, they will come,” still holds true. But if you want something different to happen when they get there, you need to pave the road.

Contributed by Kami Thordarson, Innovative Strategies Coach

Tuesday, November 5, 2013

The Handwriting Dilemma

The cycle of typing and tapping on the phone, keyboard, etc. As I settle into bed, I realize I haven't "written" anything with a pen and paper, all day. My gut races from excitement to terror as I realize there is simply no need to put pen to paper.

With the rapid increase of communication through digital devices, does it matter if we write or not? Is the future of a penned signature a fingerprint?

Common Core has removed the mandatory teaching of cursive.  A few articles highlight the importance of teaching cursive in school, In Defense of Cursive and Should Schools Still Teach Cursive. Yet, hardly anyone uses cursive as a primary form of writing. The opposite argument can be raised. If no one uses cursive anymore, then we shouldn’t teach it (clearly that is why CCSS removed it). So, with the disbandment of third graders’ write of passage, the future of penmanship as a whole appears to be misty and murky.

If writing with a pen is no longer typical, then do we even need to teach it in schools? Rather than writing in kindergarten, should kids just learn to type? Can we even extend that to touch typing on a screen rather than keyboarding?

Historically, penmanship was an art. From the Constitution, to love letters, penmanship was and still is a way to physically connect with a person by knowing that his or her hand penned the words.

Email has rapidly replaced telegrams and letters. E-cards are the new birthday notes.

The word write means to mark (letters, words, or other symbols) on a surface, typically paper, with a pen, pencil, or similar implement. Lets think about that word, “typically”, and understand that we are at a crossroads of typical and mainstream. If write means to mark, then as we type we mark the computer screen and as we write with a pen we mark paper. Yes, typically we write on paper, but in mainstream we mark on the computer. So the work write really should now include the mainstream devices we use to write which are computers.

And on the subject of writing, why do we still teach a “friendly letter” format when adults hardly send handwritten letters anymore? What we should be emphasizing is how to craft simplistic email subject lines, digital signatures, and text messages.

Communication has dramatically shifted from physical to digital. I don’t even know what ringtone is on my phone because my primary way of communicating is via text. Phone messages go forgotten because I don’t know anyone who actually leaves me messages, so when someone does I don’t even remember to check them.

Writing in school needs to keep up with the culture of communication. If we are preparing students for life, then we need to think about how they will be communicating in the world when they are adults, and thus we need to teach foundational skills that will help them in that arena.

Yet, on the flip side, there is deep historical and personal value to the physical connection between hand, pen, and paper. Productivity expert David Allen states in the New York Times article by Phyllis Korkki In Defense of Paper, “ Its physical presence can be a goad to completing tasks, whereas computer files can easily be hidden and thus forgotten, he said. Some of his clients are returning to paper planners for this very reason, he added.”
Beautifully stated, co-founder of Levenger, Steve Leveen expresses to the New York Times, “ ‘Paper reminds us that ‘we’re physical beings, despite having to contend with an increasingly virtual world,’ he said. People complain that writing by hand is slow, but that can be good for thinking and creating, he said: ‘It slows us down to think and to contemplate and to revise and recast,’ " (In Defense of Paper by Phyllis Korkki, New York Times).
The crossroads are here. Handwriting is real and physical, ideas spring to life with effort. Typing is quick, efficient, and productive. We accomplish more with less, and neatness is automatic. Handwriting connects us to the historical past, and typing pushes us forward.
Kids will rely upon texting more than email in the future. Maybe the business deals they make will be artfully crafted with emojis and Vines.
Where does handwriting stand? Where does communication stand? And how do we teach our students and children to expertly use the communication tools available to them if we ourselves stick to the tools we know?

Monday, October 28, 2013

Student Edcon: Next Steps

Student Edcon 2013 was an amazing opportunity for students to get their voice in the room! Our students did an incredible job working through the design thinking process to come up with creative and innovative ideas that bring significant change to their educational landscape. We chose three ideas that we will move forward on here in the Los Altos School District. Below are the Haiku Deck presentations created by each group along with a description of how we will work to prototype and test their ideas.

Elective Shopping: Students felt that at the end of sixth grade, they were asked to choose electives without having a clear picture of the class. Currently, they are given a short written description and choose from a list. Our prototype: a student elective fair. Sixth graders will attend an elective fair during their preview visit in the spring. There, current students of the elective classes will create a table where they will show artifacts from the class and be available for students to ask questions. Run by students for students.

Project Me: Students wanted more choice in their schedules and classwork. Our prototype: a small group of students, 4-5, will work with a teacher to design their own coursework for one semester. They will choose which classes to attend based on the class syllabus and propose ideas for how they will show their mastery of content.

Democratic Classroom: Students wanted their voices heard regarding school policies. They want to be part of the decision process and be represented in discussions of policies that effect them. Our prototype: a group of students, similar to a student council, will create a space for students to voice their issues. They will then collect data and further investigate challenges or creative ideas brought into focus by the student body. They will create solutions and proposals that they will then be invited to present at staff meetings.

Our students did an excellent job identifying issues that were important to them and then brainstorming creative solutions. We are excited to work with them as we test their ideas and build on their solutions. Stay tuned.

Watch a recap of the experience.

Contributed by Kami Thordarson, Innovative Strategies Coach

Tuesday, October 22, 2013

Storytelling Through Design Thinking

Every teacher knows the power of a good story. We weave story into our teaching to engage students and all adults have been using story to help children navigate and make sense of the world through the ages. Stories are at the heart of how our brains develop and how we learn. Storytelling has actually been proven to be interwoven into our DNA. Scientists have discovered that “if you slide a person into an FMRI machine that watches the brain while the brain watches a story, you’ll find something interesting--the brain doesn’t look like a spectator, it looks more like a participant in the action,” from Jonathan Gottschall.

In Jonathan Gottschall’s book, The Storytelling Animal, How Stories Make us Human, he says, “We are, as a species, addicted to story. Even when the body goes to sleep, the mind stays up all night telling itself stories.” He explains that most stories are almost always about people with some sort of problem and “that the human mind was shaped for story, so that it could be shaped by story.” Perfect for design thinking.

Stories are used to help you think of new possibilities. They give you tools to increase empathy and encourage self-reflection. Design thinking relies on both of these so you can imagine designs that improve the lives of others. Stories explore ideas from user research. Through the first part of the design process, story informs, drawing a picture of the present and how it exists for users. During the second part of the process, a new story is created that inspires, reframing the picture with new ideas that make things better.
From Design and Innovation Through Storytelling

Focusing on the story helps you think it through and sharing the story will help you clarify the details. Through story, you can paint a picture of the future where the people you are designing for interact with your idea. You have created a story they can participate in. Storytelling and design work together to enhance creativity and inspire innovation. As Plato once said, “Those who tell the stories rule society.”

Design Thinking is just one area where students and teachers can hone their storytelling skills. Like any skill, storytelling needs practice. Try some of these resources to improve the storytelling talents in your classroom.

Contributed by Kami Thordarson, Innovative Strategies Coach

Monday, October 21, 2013

Let's Discuss Discourse

Student discourse is not just students talking about a topic. It is the ability to discuss a topic and go deeper within that conversation to find out what students know and to identify any misconceptions. Once a misconception is identified, the next step is to have the class work through the misconceptions in a meaningful way.

In mathematics, students need to be discussing math with each other whether it is in small groups or with the whole class. These discussions can happen through various means like

problem solving, game play, whole class activities or a student asking a simple question. Another way is to have questions ready for a math discussion. These questions should be carefully written in order to promote deeper thinking and conversation. During these conversations the role of the teacher is facilitator, asking good questions and helping students work through their thoughts.

In order for discourse to happen, a classroom culture needs to be created for students to feel comfortable discussing what they know or don’t know about a math topic. They need to be able to disagree with one another or elaborate on each other’s ideas. Teachers need to be good listeners allowing students time to think through their math reasoning and allow students to talk to one another. One way a teacher can try to promote students talking to one another is to write down what students are saying during the conversation. By doing this, a teacher will be looking down at a notebook or computer which will help to avoid eye contact with students. Now I know that this might sound odd, but students are conditioned to talk to the teacher, if she is looking away they might be more inclined to address the class.

Another behavior students are conditioned to do is raise their hands to speak. My son will raise his hand at the dinner table sometimes when he wants to say something. I thought it was kind of funny at first, but now I view it differently. I recently read an article that pertains to promoting discourse. It was called “Changing the Rules to Increase Discourse,” by Lisa Brooks and Juli Dixon, published in NCTM’s journal Teaching Children Mathematics. They suggested that in order to keep discussion flowing students have to break the rule of raising their hand to speak. It allows the students to talk to one another by adding or elaborating on

the topic or learning to disagree with each other and supporting their reasoning with evidence. Before an iLearn class, which are classes for teachers after school, I had the teachers read this article for discussion. I happened to be in front of the class and asked them what they thought of the article. The first thing that I observed was multiple hands being raised in the air seeking permission to talk. I thought that it was ironic that we were talking about an article regarding raising your hand and now here are all these teachers with their hands raised. See how we are all so conditioned! After calling on a few I thought, Wait... this not how I wanted to discuss this article! We stopped, grabbed our chairs, and moved to the back of the room in order to form a circle. We continued the conversation, but the whole dynamic changed... No more raised hands, just discussion. It became more natural and more interesting as the teachers went on supporting each other in discussion and elaborating on each others thoughts.

Two of the main topics we talked about were how to build that culture and how to practice so students can get the hang of it. A few of the focus points included learning how to take turns, adding to other’s points, knowing how to disagree appropriately or ask a question of one another when you don’t understand and giving each other time to think. This all won’t happen the first time you try it. It takes time to build those skills, but it’s worth the practice. Students will begin to feel comfortable revealing their misconceptions, which will make it easier to address as a class. So the next time you want to promote discourse in your class try some of these practices. You never know what you will find out about your students’ knowledge.

Any questions? - Was your first thought to raise your hand?  :)

Contributed by Karen Wilson, STEM Coach


Brooks, L.A. & Dixon J.K. "Changing the Rules to Increase Discourse." Teaching Children Mathematics. September 2013, Vol. 20, No. 2.