# Roatan: Math in Honduras

In June of 2015, I was privileged to join my wife and several other swim school owners on a service trip to the island of Roatan, in Honduras. The purpose of the trip was to provide much-needed toys & supplies to some of the public schools there, and to raise physical fitness awareness.

Of the nearly fifty swim school owners, instructors and family members that made up our group, I was the only school teacher, therefore, I viewed the experience through a different lens than the others. I also made several connections with the teachers and was able to observe one do an outstanding job of teaching 1-digit subtraction. Watch the video below and you will be as equally impressed. The surprise for me was learning later that the class was 4th grade (in the U.S. this topic is taught in 2nd).

### My Guest Lesson

I also had a unique opportunity to teach a brief high school math lesson. I could see on the board that the lesson was about the surface area of a sphere. The teacher had written the formula A = 4πr² and there was an example showing how to calculate the area given the radius. I saw the students doing guided practice in their notebooks. The teacher learned that I also taught math and offered to have me show something on the board. From her limited English, the teacher translated for me. I kept it simple, checking for understanding via head nods after each step… I drew a sphere, then a hemisphere, then the Great Circle. I asked how many of these circles would it take to cover the surface of the sphere. We took a finger vote. Most of the class claimed “2.” I claimed that the teacher already showed them… in the formula … 4 circles (πr²). I then applauded the teacher for knowing that. (You can see me building her up to her students, in the picture below. They all applauded her.)

### Schools in Roatan

25% of all Roatan children do not have the means to attend to school. Of those that do, 30% do not continue beyond the 6th grade. This will change as the economy improves. Thirty years ago, there was no electricity and no paved roads on the island. Progress on Roatan has a strong upward trajectory that can be accelerated with a little bit of help.

### Our 2015 Visit

We visited six schools:

• Victor Stanley West End School
• Froylan Turcios School
• Escuela Juan Lindo
• Garby Nelson
• Thomas McField
• Isidro Sabio

We provided donations from the swim school owners and from the clients of the schools.The outpouring of generousity was amazing. The supplies ranged from desks to soccer balls to toothbrushes to backpacks.

Another intention of the trip was to provide physical fitness awareness. The kids had a great deal of fun with both the new exercises and the activities.

Many of the students greeted us warmly. We learned that many kids had not seen pictures of themselves, so they got a kick out of us showing them their images on our phones.

The trip ended with the Swim Celebration on the beach at Half Moon Bay in the West End. I was surprised on an island how children didn’t know how to float. The lessons were readily accepted, as was the swimming gear (swim suits, intertubes and goggles). As you can see, my wife fell in love with the Honduran children.

Our group will be returning to the amazing land and people of Roatan in the summer of 2017.

# Twitter Math Camp 15 Re-Cap

What happens at Twitter Math Camp never stays at Twitter Math Camp!

How can it? We all met through Twitter, speak through blogs, ride a communal wave of a passion, ache to change the world through math education, and respond to the annual call of Lisa Henry (@lmhenry9) to gather each summer for the most exhilarating, unique and educational professional development event that any of us have ever experienced. Collectively, we form the universe know as the Math Twitter Blogosphere (#MTBoS). With this kind of excited learning and a vehicle to share it loudly with the world, there is no way to keep TMC a secret.

So in this passionate, collaborative, spirit, here is my Re-Cap of TMC15

{Note: All videos shown here were recorded by Richard Villanueva}

GOING DEEPER WITH DESMOS Session
Jed Butler (@MathButler), Michael Fenton (@mjfenton), Glenn Waddell (@gwaddellnvhs), Bob Lochel (@BobLoch)

The “Morning Sessions” of the Camp consisted of 2-hour sessions that ran each of the first three days. Each 3-morning session was based on a topic. I attended the one on Desmos, the premier, free, online, graphing calculator. This was an enormously productive time that inspired me to SCHEDULE in advance, where and when to use Desmos in my curriculum this year. Here’s what I learned about Desmos ….

1. Tours: These are built-in tutorials that walk you through the Desmos basics of Graphing Equations, Creating Tables, Lines of Regression, and Restrictions (domain & range). Just click the question mark in the upper-right corner.
2. Desmos Bank: A communal site where teachers can share Desmos ideas and activities.
3. Activity Builder: Eli Luberoff (@eluberoff), the founder and CEO of Desmos made a guest appearance at our session to announce the launch of the Activity Builder. In essence, this allows teachers to create lessons, constructed of a sequence of Desmos activities. Trust me, YOU WANT TO CHECK THIS OUT.
4. Student Accounts: If students have a Google account (which all of mine do), they can log into Desmos through Google, which allows them to save their work and send their products to the teacher. That’s going to happen in my class this year.

GEOMETRY, Not an Island
Jasmine Walker, (@jaz_math), Burlington, Vermont

Jasmine started her session with a statement that I very much agreed with: “Even if your school or district has not adopted an integrated curriculum, you should still teach geometry as if it has. Geometry is not an island; we should not leave algebra behind.”

She then posed the question, “How do you start the year in Geometry?” for which the room had a very uniform answer … with vocabulary. This led the conversation on how to start the year with rich math tasks that link algebra to geometry. There was not a great deal of time for solutions, but the conversation brought me back to the Desmos activity builder. Geometry, Algebra & Vocabulary can all be brought together with a Desmos activity in which students need to generate geometric shapes on a coordinate plane, with restricted equations.

WHAT DO YOU THINK AND WHY? Supporting Students in Sharing their Ideas
Dr. Ilana Horn (@tchmathculture)

Dr. Horn spurred a terrific conversation among a large audience about how we, the various teachers in the room, support students in the sharing of their thinking in math class. The class had some wonderful ideas, however, what struck me most was not anyone idea, but the fact that so many ideas existed in a collective body of teachers. It truly is not a matter of knowledge, but a matter of will in getting students to work together and discuss their ideas. I was also impressed in Dr. Horn’s use of Polls Everywhere. I saw the power of the simulataneous viewing of the classes’ thoughts. I have been contemplating the use of Pear Deck (a similar platform) in my class.

Teaching the 8 Practices
Me! (@MathProjects)

I taught a session on teaching the 8 Standards of Mathematical Practice, in which I shared my SMP Posters, their corresponding Wordles, and the explicit teaching of the practices through “Dual Targets.” (my blog post forthcoming)  Meg Craig (@mathymeg07) posted about the implementation of #SMPTargets in her own classroom.

Growing Our Practice  (Keynote #1)
Dr. Ilana Horn (@tchmathculture)
(video Part 1, Part 2)

Dr. Horn is well known for studies on teacher collaboration as well as student collaboration, therefore, she often talks about how teachers think about teaching. She once again delivered on that point through the lens of how teachers’ perspectives affect their professional growth, parsing out the difference between good teachers and great teachers into three key qualities:

• Problem Frames
• Representations of Practice
• Interpretive Principles

The great teachers have …

• Problem Frames that are actionable,
• Representations of Practice that include more student voice and perspective, and
• Interpretive Principles that focus on connections among teaching, mathematics and student understanding

In other words, great teachers do not spend a lot of time and energy discussing things they have no control over; rather, they ponder how students think about and interact with mathematics, and what how the lessons and activities affect their learning. So Dr. Horn called for …

• Teacher Agency
• Empathic Reasoning
• Ecological Thinking

This resonated throughout a room full of people bent on “growing their practice.”

Math From the Heart, Not the Textbook (Keynote #2)
Christopher Danielson (@Trianglemancsd)
(video Part 1, Part 2)

Christopher laid down the inspirational challenge: “Find what you love. Do more of that.” He shared with us how he loves ambiguity and, therefore, was OK with playing the game of Which One Doesn’t Belong? For example, what students would choose and why in the set of four figures below, will offer up multiple answers.
Christopher is also the author of Common Core Math for Parents for Dummies. A much needed resource in responding to the darkside of social media.

“Find what you love. Do more of that.” — Christopher Danielson

Teacher Woman  (Keynote #3)
Fawn Nguyen, (@fawnpnguyen)
(video Part 1, Part 2)

Fawn did here what Fawn does best: She made us all feel wonderful about being teachers. She humorously poked fun at the tweets that many of us sent her, but also seriously shared her personal trimphs and tragedies. In the end, our diminutive twiter celebrity grew huge with inspiration. She tearfully read a complimentary letter from a grateful student, and then told us of her sister who is an engineer. An emotional Fawn, claimed “She makes more money than me,  but she doesn’t have that letter!”

“She makes more money than me, but she doesn’t have that letter!” — Fawn Nguyen

My Favorites
Several times throughout the Camp, there is time given for people to share a 5-10 minute presentation of a technique, activity or routine that they love. There were nearly two dozen amazing ideas.

Two of them I have already implemented in my class …

High 5’sGlenn Waddell (@gwaddellnvhs): Glenn was right. Offering the High 5’s at the door does more for my mood and mental preparation for the class than it did for the kids.

Music Cues, Matt Vaudry (@MrVaudrey): Playing Mission Impossible at the beginning of class and the Benny Hill Theme song at the end has drastically improved the time spent retrieving and cleaning up materials.

and two others I intend to use in the future …

Egg Roulette, Bob Lochel (@BobLoch): This looks to be a very engaging activity on probability and on making and critiquing conjectures.

Student Videos, Princess Choi, (@MathPrincessC): Having students make videos on math concepts, and then post them to a place where they may “like” and “comment” on each others is cutting edge.

I presented two of my own Favorites …

Neuron Stickers, Brain Surgeons & Wrinkle Sprinkles:  These are vehicles that that I used to cultivate a Growth Mindset in my students last year. (my blog post forthcoming) @mathymeg07 blogged about Strengthening a Dendrite and how to get inexpensive posters made.

Rally for Roatan: A pitch for the altruistic effort to bring textbooks and instructional supplies to the school district of Roatan, Honduras, and the roll-out of my new web page to support it.

MATH COACHES Roundtable
Chris Shore (@MathProjects), John Stevens (@Jstevens009), Chris Harris (@CHarrisMath), Hedge (@approx_normal), Jennifer Bell (@jkjohnsonbell), Nanette Johnson (@Math_m_Addicts), Robert Kaplinsky (@robertkaplinsky), Shelley Carranza (@stcarranza)

We eight math coaches had a wonderfully transparent roundtable discussion of what was working and not working at our sites. I was helpful to hear about so many successes, and to know that we shared many of the same issues. Listed below are the bulleted notes from that exchange.

“How do I move teachers along the WHY train?” — Nanette Johnson

Successes

• 100% Handshake Introduction
(Introduce self to every math teacher with a handshake)
• Modeled Number Talks in 150 classes in 2 months
• Acceptance of math coach at 16 schools
• Teacher input (What do you think?)
• Liaison/Advocate for teachers with District
• Teacher invitation and openness
• Self-Growth
• Started Math Coach Network
• Model Lessons (Geogebra, Desmos)
• Teacher understanding of Common Core as teaching students to “Think & Communicate”

Resources:

• #educoach: Wed 7pm Pacific
• #k12mathcoach: 2nd & 4th Wed 6pm Pacific
(starting in August 2015)
• #elemmathchat: Thurs 6pm Pacific

Issues

• Dismal lack of content knowledge in some cases
• Missing teaching in the classroom
• Coaching is more about psychology than math.
• Drinking from a firehose, but only able to spit it back out
• How do we collect data on effectiveness
(Woodruff scale: 10 things)

Burning Questions:

• How do I move teachers along the WHY train?
• How do I use Behavior Economics to nudge change?
• How do you measure effectiveness of PD?
• What data do we have to show that we are effective?
• How do I support myself at my getting better at my job?

The Side Talks
I had several conversations throughout the Camp, but two that stood out were with …

Lani Horn (@tchmathculture): We finally had our long overdue conversation about the structure of collaborative student groups. Dr. Horn wrote THE book on this topic, Strength in Numbers. I have always used a great deal of group work, and recently Lani’s emphasis on “status” in the class has influenced my thinking a great deal. We had the controversial discussion regarding grouping homogeneously, heterogeneously or randomly which finally settled the issue in my mind. I will share the results of that dialogue in a future post. #cliffhanger

Edmund Harris (@Gelada): Edmund and I love comparing American & British education systems. (Dr. Harris is originally from Britain and now teaches at the University of Arkansas). This year, he was very hot on the treatment of homework in both countries. He insists that rather than it being either the traditional, boring rote or the new, mind-crushing, “common core” problems that end up on haters’ Facebook pages, that math homework should be a “joyful meditation.” I love this thought; now comes the challenge of making it happen for my students.

Edmund also is the Illustrator of a new book coming out, Patterns of the Universe, A Coloring Adventure in Math and Beauty. He is my go-to expert for anything that deals with Geometry, so I cannot wait until this book comes out. The preview below of his illustrations will get you just as excited.

“Homework should be joyful, meditation.” — Dr. Edmund Harris

TMC15 was a phenomenal four days at Harvey Mudd College in Claremont, California. TMC16 will be at Augsberg College in Minneapolis,MN, July 16 – 19. I can’t wait to reconvene with this crew, so that, as one participant shouted …

“My brain will explode with awesomeness!”

And just for kicks …

# CA Mathematics Network Forum, 2015 Re-Cap

The 2015 California Mathematics Network is a community of math education leaders from twelve regions in the State. This Conference focused on the NCTM publication Principles to Actions. The book is an amazing resource that discusses what needs to be done in math classes, and what actions need to be taken by teachers and administrators alike to make that happen. It should be read by anyone who has an investment in math education. A good primer is p 5, 10, & 109-116, or check out the Executive Summary. Following are some terrific ideas from the conference speakers on how to implement these Principles.

#### The Best of the Common Core Closes the Achievement Gap — Dr. Lee Stiff, former NCTM President

• The Achievement Gap can best be narrowed through Effective Teaching of the CCSSM Practices.
• Where do these effective teachers come from? … “from our good work!” (as instructional leaders)
• The primary purpose of Principles to Actions is to fill the gap between the adoption of rigorous standards and the enactment of practices, policies, programs, and actions required for successful implementation of those standards.
• NCTM Guiding Principles
(from Principles to Action)
Teaching and Learning
Access and Equity
Curriculum
Tools and Technology
Assessment
Professionalism
• NCTM Teaching Practices
(from Principles to Action)
1. Establish mathematics goals to focus learning.
2. Implement tasks that promote reasoning and problem solving.
3. Use and connect mathematical representations.
4. Facilitate meaningful mathematical discourse.
5. Pose purposeful questions.
6. Build procedural fluency from conceptual understanding.

7. Support productive struggle in learning mathematics.
8. Elicit and use evidence of student thinking.
• Student placement and support should be based on DATA not DEMOGRAPHICS.
• We create the gap!!

#### Teaching Practices that Support Student Learning of Mathematics — Peg Smith, University of Pittsburgh

Dr. Smith had us read through a well-known task, the Hexagon Train, and then analyzed it through the lens of each of the Teaching & Learning Principles in Principles to Actions (Summarized Below):

1. goals
3. representations
4. discourse
5. purposeful questions
6. procedural fluency

7. productive struggle
8. evidence of student thinking

• “What you put in front of the students frames their opportunity to learn the mathematics.”
• It’s time to break out of the “postage stamp” lesson plan, (the homework, & examples fit in a little box), and write analytical, anticipatory lesson plans. (This one needs a cute name, too)
• It’s difficult for teachers to use a high level task. It’s even more difficult for them to use it well.
• Decrease the complexity of language without decreasing the cognitive demand of the task.
• “Never Say Anything That a Kid Can Say.” (Article)
• Writing “SWBT” objectives limit what students learn. Is the goal really to be able to find the length of the hypotenuse or to understand the relationship of the areas of the squares formed by the three sides of a right triangle?
• Dr. Smith is the co-author of 5 Practices for Orchestrating Productive Discourse in Mathematics Class.
• Dr. Smith shared this Principles to Action Tool Kit:

Dr. Smith then asked us to restructure a standard series of textbook questions into a more robust task. The conversation at my table was very rich. It was a briefer version of a lesson makeover, and would be an awesome PD activity.

#### Smarter Balance Update — Mary Tribbey & Jane Liang

This slide makes two BIG statements:

1. The Red Dot () is along a timeline from the start of the assessment initiative to full implementation. We are still in the early stages of perfecting it.
2. There do exist Interim Assessments that few schools (including mine) are using to check for student readiness.

This day was the first I heard of the scaled score for the reporting of the test. It appears that there will now be some reporting on the standards as well as the claims, after all.

#### Equity-Based Teaching Practices — Karen Mayfield-Ingram, EQUALS Program, UC Berkeley

1. Going Deep with Mathematics
2. Leveraging Multiple Mathematical Competencies
3. Affirming Mathematics Learner’s Identity (multiple access points)
4. Challenging Spaces of Marginality (diminish status within class)
5. Drawing on Multiple Resources of Knowledge (including culture and experience)

Lesson: “He Was Suspended for Being Mexican” (excerpt from The Impact of Identify in K-8 mathematics Learning and Teaching) This was an anecdote of a teacher who took a students statement, “He was suspended for being Mexican,” and turned into a statistics lesson in which the students had to analyze data to determine if the school policies truly were racist or not. While we can’t tie every topic into a student-oriented context, I think it is a powerful idea that should be done more often.

#### Technology & Computation — Joe Fielder, Cal State Bakersfield

• All computation outside the classroom is done by a machine.
• Machine computation is mostly done with spreadsheets.
• Hand calculations are only done in math classes. (referenced TED talk by Conrad Wolfram)
• If we are going to teach students mathematics that is relevant beyond the college entrance exam, we need to give explicit instruction on the tools of computation.
• Dr. Fiedler is currently working with the college board to change the SAT to reflect computations done by hand-held graphing calculators.
• The introduction of the first scientific calculator 1972 was controversial, because teachers were worried that students would no longer be able to use tables.
• “Students are idle, indifferent, irresponsible in response to absurd work. This is a rational response!”
• There is no change without a loss. If there is no loss, there is no change. Similarly, literacy diminished the need for memory, but we still teach students to read and write.
• Yes, part of education’s job is to pass on old knowledge, but it’s not the entire job. It’s time to get with the times.

#### BREAKOUT: Exploring the Common Core Statistics & Probability Standards — Jim Short, Ventura County Office of Ed

• “Statistics means never having to say your certain.” The irony is that this is what makes math teachers uncomfortable with stats.
• Teachers are avoiding the teaching of statistics, but the ponderous of the Performance Tasks on State Tests are based on Statistics and Data Analysis.
• Statistics is more important than Calculus. (referenced TED talk by Benjamin Arnold)
• From the GAISE Report,
4 Components of Statistical Problem Solving
I.   Formulate Questions
II.  Collect Data
III. Analyze Data
IV. Interpret Results
• You aren’t teaching statistics unless you are teaching modeling.Here are some great tools that we used in the session to generate statistical displays in a spreadsheet:
Geogebra {box-n-whisker}

Core Math Tools {NCTM}
=norminv(rand(), means.d.)” {Excel Macro for generating a set of normalized data}

#### BREAKOUT: The Right Answer is Not Enough — Ivan Cheng, Cal State Northridge

• What the teacher assesses is what the students think that the teacher values.
• How is “doing math” defined differently under Common Core versus NCLB? How you answer that questions, determines how you teach and assess under the new standards.
• After a test, if the teacher can’t state what the student misconceptions are, then the teacher needs to do some more digging.
• Teachers should use assessment questions that intentionally reveal misconceptions.
• Why “a” student missed a question is as important as which question they missed.
• Clicking Smarter Balanced ASSESSMENTS (in SBAC navigation bar) will take you to documents that map targets to standards.
• “Think about getting through to the kids instead of getting through the textbook.”
• This sample question demonstrated why the students have issues with the new assessments. The students instantly think that the answer is “20,” because x = 20. Since 20 is not a given situation, they often choose “D: Neither.”

#### My Big Take-Aways

• The achievement gap can be closed by the effective teaching of the Math Practices.
• Two Big Words kept coming up: Meaningful & Equity. Equity is achieved by giving all students access to meaningful, high-level mathematics.
• Get with the times, and start using technology in order to move from computation to deeper, higher mathematics.
• There are some amazing tools available for Statistics tasks. This is a pervasive topic that needs serious attention and support.
• Our assessments communicate what we value. The assessments are changing, because our goals are changing. Therefore, we teachers must change our values and practices.
• We should all read Principles to Action.
• The Region 10 Team is an amazing group of intelligent, passionate people. I look forward to seeing how we will put all these principles into action.

# NCSM 2015 Re-Cap

I spent a terrific week in Boston for the 2015 NCSM & NCTM conferences. I am recapping the NCSM sessions here. I already summarized the NCTM sessions in a previous post.

As with my other Re-Cap, I have summarized each session with some simple (•) bulleted notes and quotes to encapsulate my major take-aways, and occasionally a brief italicized commentary.

While I have been to several NCTM conferences, this was my first NCSM trip. For my new position as math coach, this was experience was very worthwhile.

#### What the Research Says About Math Coaching? — Maggie McGatha

• Positive, small student increase in 1-2 years, strong spikes after 3-4 years.
Math Coaching works, but you must be patient. This was my biggest, most encouraging take-away of the conference.
• Positive teacher growth on incorporating Questioning, Engagement, Conceptual Understanding, Group Work, Discourse & Technology.
• Spectrum of Coaching
(least directed is most effective, all are needed)

most directed ——————————- least directed
Model lessons          Co-Planning           Data Reporting
Resources                Co-Teaching           Reflecting

Ironically, the most directed (lesson resources) is what teachers request most often, even though it was the least effective service from math coaches. It still showed teacher growth and student improvement, so this is the logical place to start with teachers. As soon as possible, though, it is better to work side by side with the teachers on these lessons.  The ultimate coaching service, though, appears to be the debrief… having teachers look at student results and contemplate their effect on student learning.

#### Achieving Equity: Instructional Strategies to Reach All Students (Chicago) — Ruth Seward, Jessica Fulton, Lynn Narasimham

• The third largest district in the country has a very structure, organized, intentional professional developement program.
If a district this large can provide sustained PD for its teachers, then my district should be able to do the same. We just need a plan and a system to implement it. My district has both, but they need to be revisited to include some of the following.
• Focus on Engagement, Application and Communication
• Accountable Talk… Just as teachers should question more than tell, we should have students do the same with each other, also.
1) Read aloud to a peer.
“What is the question in the problem?”
3) Read it a third time.
“What information do you know and not know?”
• Hierarchy of training:
PD is given to Admin as well as Teachers.
PD for teachers includes Elbow Coaching (Co-Planning, Co-Teaching, Co-Reflecting)
• The Five Dimensions of Mathematically Powerful Classrooms

• We were also shown an example of the types of activities that are promoted in their teacher training. We were asked to place the Decimal/Percent cards in order from least to greatest, and to fill in any blanks. Then we had to match the set of Fraction cards, followed by the Area Model cards, and finally the Number Line cards.
This would be a great activity to open the year with in ANY class, even an upper level, in order to accelerate number sense and set norms for group work.

#### Engaging ALL Learners in Mathematical Practice through Instructional Routines — Amy Lucenta & Grace Kelemanik of the Boston Plan for Excellence

• The Standards for Mathematical Practice create open doors to struggling students, not walls.
This is such a simple, yet profound concept. It was the heart this presentation, and one of the best principles pitched at the conference. I’m a fan, because it is one of the three principles that I shared in my presentation at NCTM .

• Not all SMPs are created equal. #1, followed by #2, 7, 8.
I have heard many people say that the 8 Practices should be a shorter list. It was interesting to see their list.

#### Hey! What’s the Big Idea? — Greg Tang

• Progressions is the Big Idea?:
Concepts -> Algorithms -> Speed
Greg really pushed for a balanced, reasonable approach to teaching math. I have always emphasized the first two, but was challenged to put more effort into the back end. This was one of the Biggest Ideas that I brought home.
• Number Sense is Key, and can be enhanced through number games.
I am now addicted to Kakooma
• “Generalizing your thinking is what makes you smart.”

#### Reinventing Algebra in a Common Core World — Eric Milou

• Provocative Statement #1: Dr. Milou laid out an Algebra sequence that pushed the introduction of Quadratic functions to Algebra 2.
• Provocative Statement #2: Teachers need to to start a grassroots revolution to address the Common Core’s failure to limit the bloated list of standards in high school, since no revision/feedback mechanism exists.
I was very impressed that NCSM allowed a dissenting view, and I loved the courage with which Dr. Milou spoke. While I find his suggestion having merit in terms of math progressions, I don’t see how it  addresses the glut of standards, so I agree with him that there needs to be a feedback mechanism to address that issue.

#### Sense-Making: The Ultimate Intervention — Janet Sutorius

• Removing the mathematics from context and focusing on procedures prevents students from using their own common sense and sense-making abilities to do mathematics. Struggling students need a contextual framework the most.
I have always said… naked math comes last.

#### Hot Topics: Intervention — Matt Larson

• Do not pull struggling students out from class. Give them additional learning, instead.
This was a round table discussion with a big name in the field of math ed. He described some field studies he was involved with in Chicago regarding elementary intervention structures. The big take-away here was to not have intervention students miss class time. Build the time into the day when they receive additional instruction on unmastered topics, and give those who have mastered the topic an enrichment activity.

#### Occam’s Razor — Eric Hart

• Focus on the Math first (methodology second)
This echos what I learned from William Schmidt, about focusing on the mathematics, not the methodology.
• “If we could switch from telling to questioning, we would change the world of math education.”
A college Professor said this! In public! I pressed him on this statement, which I whole-heartedly agree with, but pointed out the obvious … college math is taught almost entirely through telling. His response was, “That is changing.”
• Which form of the Quadratic Formula is better? Doesn’t the less conventional one make more conceptual sense?
This pic got a lot of response on Twitter.

• Students in other nations do not spend as much time on factoring as U.S. students. They use the Quadratic Formula to get factors them plug them into the equation.

#### Mathematic Modeling with Strawberries and Video — Sean Nank

• Sean had us participate in a modeling task that involved a video of himself cutting strawberries. The task walked us through each step of the Common Core’s definition of modeling:
1. Identifying variables,
2. Formulating a model by creating and selecting representations that describe relationships between the variables,
3. Analyzing and Performing operations on these relationships,
4. Interpreting the results of the mathematics in context,
5. Validating the conclusions,
6. Reporting on the conclusions and the reasoning behind them.

The question was simple, “How long will it take to cut the strawberries?” The task, however, was rich and robust. While Dr. Nank allowed the lesson to be very student driven, he still paused before each of the 6 steps above, to direct us in the next segment. It was a great demonstration of how to scaffold the teaching of modeling, instead of the typical errors of “Here kids, now model.” or the “Let me show how modeling is done.”

• Marilyn Manson Pedagogy: “Just shut up and listen.”
Dr. Nank shared an interesting anecdote. He said after the Columbine shooting, Marilyn Manson was asked what he would say to the kids. He claimed that he wouldn’t tell them anything, he would  “just shut up and listen.” Sean was encouraging us to do the same while the students are working on the various components of modeling.

#### PAEMST Seminar for Awardees of The Presidential Award for Excellence in Mathematics and Science Teaching — Dan Meyer

• Dandy Candy Lesson
I have always loved this task. Dan took it so much deeper than I had imagined from his post on it. It was a delicious pleasure to participate in it with its creator.
The conversation at my table of instructional leaders was how to get teachers to do lessons of this richness and quality. Our teachers back home all readily admit that they need as much scaffolding in teaching these kind of lessons as the students do in learning them.
• When leading students through a task like this, wait for their questions. “Don’t give away too much, too soon. You can always add, but you cannot subtract.”
• Dan shared Sean Nank’s/Common Core’s Definition of Modeling. (He also has a great post on modeling.)
Dan also probed us for our take on it. There was consensus at my table that the definition was solid, but that modeling did not always have to be that comprehensive or limiting. There was also consensus that creating mathematical models from a given context to this degree needs to be done far more often in classes.
• I met up with Jerry Young of Oregon, a fellow awardee from 2001 whom I really connected with in Washington DC, some 13 years ago. This was a treasured highlight of the trip.

As you can tell, it was a great trip, from which learned a great deal. I am already looking forward to NCSM 2016 in San Francisco.

# NCTM 2015, Boston Re-Cap

I had the wonderful opportunity of spending a week in Boston for the 2015 NCTM & NCSM conference. I am recapping the NCTM sessions here, and the NCSM sessions in another post.

Since there was so much information, I have summarized each session with some simple (•) bulleted notes and quotes to encapsulate my major take-aways, and occassional a brief italicized commentary.

This was an enormously worthwhile trip. I highly recommend that you get yourself to San Francisco in April 2016, if you can.

#### NCTM President’s Address: Five Years of Common Core State Mathematics Standards — Diane Briars

• “College and Career Readiness” in math calls for Statistics, Discrete Math & Modeling.”
• Standards are not equal to a curriculum.
We need to pay more attention to the tasks & activities through which the students experience the content, rather than simply focusing on the content itself.
• 75% of teachers support Common Core, but only 33% of parents support it, and 33% of parents don’t know anything about it.
So we have to get the word out.

#### What Decisions — Phil Daro (1 of 3 writers of CCSSM)

• “Don’t teach to a standard; teach to the mathematics.”
This was the most challenging statement of the conference for me, mostly because I’m still struggling to wrap my mind around it. I get what he means, but I have been so trained to state an objective on the board and bring closure to that lesson. He shared that Japanese lesson plans are simply descriptions of the math concepts of the unit rather than the typical American model of objective, examples and practice sets.

#### The Practices in Practice — Bill McCallum (1 of 3 writers of CCSSM)

• Students understanding what WILL happen without doing the calculations is an example of Using Structure.
I took this back to my classroom and immediately applied it in the students’ graphing of quadratic functions. One of the more practical things I took from the conference.
• “A student cannot show perseverance in 20 minutes. It is done day after day.”
• Noticing & Wondering applies to teachers looking at student work as well.
Dr. McCallum was referencing an instructional practice made well-known by Annie Fetter of the Math Forum through which students are asked to closely analyze mathematical situations. He was calling on teachers to focus on and analyze student thinking (not simply answers) just as closely.

#### Five Essential Instructional Shifts — Juli Dixon

• Shift 1: Students provide strategies rather than learning from the teacher.
• Shift 2: Teacher provides strategies “as if” from student. “When students don’t come up with a strategy, the teacher can “lie” and say “I saw a student do …”
• Shift 3: Students create the context (Student Generated Word Problems)
• Shift 4: Students do the sense making. “Start with the book closed.”
• Shift 5: Students talk to students. “Say Whoohoo when you see a wrong answer, because we have something to talk about.”
I felt that I do all of these, but that I have been ignoring Sgift #3 this semester. Dr. Dixon compelled me to give this more attention again.

#### Getting Students Invested in the Process of Problem-Solving — Annie Fetter & Debbie Wile

• Teachers must stop focusing on answer getting before the students will.
• Honors Students are used to a certain speed and type of outcome, so they need a different type of scaffolding when it comes to problem solving.
• “If you are focused on the pacing guide rather than the math, you are not going to teach much.”
This was one of several comments, including Dr. Daro’s, that bagged on the habit of being too married to a pacing guide of standards.

#### Motivating Our Students with Real-World Problem-Based Lessons — Robert Kaplinksy

• To students: “I will only give you information that you ask me for.”
• Chunking tasks (Teacher talks — Students Think/Pair/Share — Repeat) was demonstrated to allow student conjectures, critiquing reasoning and high engagement.
Robert modeled his “In-n-Out” lesson. I have seen this several times, but I never get tired of it, because it is awesome. Every time I have witnessed this lesson, teachers cheer when the answer to the cost of a 100 x 100 Burger is revealed. I have never heard this from someone looking up an answer in the back of a textbook. Also, Robert expertly demonstrated how a lesson like this should be facilitated in class by chunking and by getting the students to think of what they need to know.

#### Getting Students to Argue in Class with Number Sense Activities — Andrew Stadel

• “As the teacher, I feel left out if I don’t know what my students are thinking and discussing.”
• Discussion techniques
Andrew is known as Mr. Estimation 180.” In this session, he showed how to bring SMP #3 into a number sense activity. The new one that I learned from Andrew here was having students stand up … those that choose A face left, B face right, C face forward. Then find someone near you who agrees and discuss. Find someone who disagrees and discuss. That’s Bomb!
• Calling for Touch Time with the Tools
In other words, let’s get the kids measuring with rulers, constructing with compasses, building with blocks, graphing with calculators.
• Chunking tasks to allow student conjectures, critiquing reasoning and high engagement, as I saw with Kaplinksy.

#### Using Mathematical Practices to Develop Productive Disposition — Duane Graysay

• Duane and other educators of Penn State created a 5-week course with the intent of developing a productive disposition in mathematical problem solving.
There were a lot of data showing the effectiveness of this program which focused on teaching the 8 Math Practices. The most amazing and provocative result was shown by this slide in which student felt that the math was actually harder than they thought before the course, but that they felt more competent.

(SA = Strong Agree, etc)

#### Shadow Con — A Teacher Led Mini-Conference

• There were six worthy educators from the Math Twitter Blogosphere (#MTBoS) that each offered up a brief 10-minute presentation. The uniquely cool aspect of these talks is the Call to Action at the end of each. In other words, you have to do something with what you learned.
• Michael Pershan’s talk: Be less vague, and less improvisational with HINTS during a lesson. Instead, plan your hints for the lesson in advance.
This one resonated most with me, because I once heard that Japanese teachers have a small deck of cards with hints written on them. To draw a hint card, students have to first show effort and progress, then they may draw a hint card. They must use each hint before they may draw another. I accept Michael’s call to action.

#### Ignite — Math Forum

• These were a series of 5 minute/20-slides mini-presentations that were more inspirational than informational. Apparently they are part of a larger movement (Ignite Show), but the folks at Math Forum have been organizing these at large conferences for a few years.
If want to get fired up about teaching math, these sessions definitely live up to their name.

Can’t wait for next year!

# A Call to Substance, First Interview with Dr. William Schmidt

In March of 1998, during the inaugural year of The Math Projects Journal, we had the unique opportunity to publish our interview with Dr. William H. Schmidt, of the University of Michigan. At the time, Dr. Schmidt was the National Research Coordinator and Executive Director of the U.S. National Center which oversaw participation of the United States in TIMSS. The results of the TIMSS report directly led to the developement of the Common Core 20 years later, which is why Dr. Schmidt is nicknamed “the Godfather of the Common Core.” He is also widely published in both journals and books on mathematics education.

We had the opportunity to interview Dr. Schmidt again about the rollout of the new curriculum. Before we post the current interview, we thought it would be valuable to reprint what Dr. Schmidt had to say in the early years of the research. He emphasized focusing instruction on conceptually understanding and higher order thinking skills, rather than on methodology. This is an important message now more than ever with so many untested techniques and ideologies being promoted widely on the internet. This message heavily influenced the trajectory of MPJ‘s lessons and my own classroom teaching. I hope it does the same for yours.
*************

MPJ: Can you give an example of a model lesson from one of the top achieving countries, either Germany or Japan, which are the focus of the videos?

Dr. Schmidt: If you look around the world, there just isn’t a single way to teach that is dominate among the top achieving countries. Some of them are very didactic, lecture-oriented classes. Some of them are like the kind that you see in the Japanese tapes. If teachers know their mathematics well, they can be just as engaging through a lecture format, as they can teaching as the Japanese do. It is very clear to me that there isn’t one way to do this. Instead, the more analysis that I do, the more I believe that there are some principles involved here that just might go across countries.

MPJ: What is the common thread?

Dr. Schmidt: I think the common thread that makes for the top-achieving countries is pure, honest-to-goodness mathematical substance. If the teachers really know and understand the mathematics, then they bring that to the students, through whatever means they know best. Also, a large part of this idea is to develop this stuff conceptually and not just algorithmically. I think many people misunderstand the Japanese videos. It is not so much the methodology, as it is the mathematics. You watch those lessons and the instructor really understands the mathematics, engaging those students in more ways than we do in this country.

MPJ: So, if a teacher were to do a dog-n-pony show lecture with drill-n-kill practice, and do it well, would it work?

Dr. Schmidt: The dog-n-pony show lecture, yes; the drill-n-kill, no. That’s what I said about there being some principles. I think the common element is a clear understanding of the subject matter and then going through it much more conceptually than algorithmically.

MPJ: Can you give us a model to how to teach math conceptually rather than algorithmically?

Dr. Schmidt: A U.S. lesson typically starts out with the algorithm. For instance, there is the example in the videos of a guy teaching geometry. He says to the kids, “Here are two supplementary angles, one is thirty, how much is the other?” A student says, “a hundred and fifty.” And the teacher says “Good, now why is it that?” And her response is, “Because they are supplementary.”

Instead, conceptually, you could show them that if they measure a straight line, it’s always one hundred and eighty degrees. Then they realize that if they put a line anywhere its going to cut it into two parts. That’s conceptual; you start with understanding why, so if you forget the stupid name, supplementary, and you see a line with an angle you’ll know what the other one is. That’s the difference.

MPJ: How is a strong conceptual understanding of the mathematics developed among teachers?

Dr. Schmidt: It comes from two sources. In some countries, they must major in these fields. The other thing we don’t think about is that they are products of their own systems. For instance, Japanese teachers don’t necessarily take more mathematics at the university level than we do. But look at what they already know before going to the university. They are already ahead.

MPJ: In regard to the things that our readership is looking at, active learning, projects, manipulatives, do you have any models from these other countries, or that you think could be done here?

Dr. Schmidt: You don’t find very much of that anywhere else. They seem to be uniquely American inventions, especially the cooperative learning. We asked teachers how much they use groups, and it’s pretty much nonexistent. We are too much into the methodology in this country, and we miss the substance. We start talking about small groups and manipulatives and it just becomes process. Therefore, the substance behind it gets lost in the shuffle. And for a lot of these ill-prepared teachers, that’s what they grab onto because that’s what they understand.

MPJ: We hear that the US teachers assign more homework and spend more class time dealing with homework than the top achieving countries.

Dr. Schmidt: The dominate activities in the U.S. lessons were reviewing homework and doing seat work. One thing that was startling is that the typical American lesson had only 10 minutes or less of instruction.

MPJ: What role does homework play in other countries?

Dr. Schmidt: It varies a lot. Japan doesn’t give a lot of homework, but the kids study for the next lesson. There’s a difference, of course. Studying is what you do at the university, and homework is what you do in grade school. But Japan is unique. Worldwide, homework and seat work are still the dominate activities. I think if you do that and you do it well, and develop the topics conceptually, it can work.

MPJ: Is this a curriculum issue instead?

Dr. Schmidt: It is the core issue, but just putting that in place by itself wouldn’t work. You have to help teachers teach in ways that engage kids.

MPJ: So, that is something that teachers could start doing today. We could focus on engaging students and developing topics conceptually?

Dr. Schmidt: That is my point. We must start paying much more attention to the subject matter and teach it more conceptually and less algorithmically. And that is why we are in a catch-22. The Japanese teachers grew up in their system seeing math developed conceptually, no matter what they learned at the university level. For our teachers it is a lot more difficult; they have to break out of a mold that they’ve been put into. But I think that is something that teachers can do — Get off the algorithmic side. Don’t just give an equation and when a kid asks why say, “Because that’s the equation.” Try to get them to understand what lies underneath some of this stuff.

MPJ: It seems that, chronologically, you are suggesting a lesson should move from concept to algorithm to application.

Dr. Schmidt: A lot of the lessons that we’ve seen, like in France and such, start out with an application as a motivator. An example is a science one about transformers. They started out by looking at a map of the city and looking how electricity would flow. This got them hooked on the issue, then they hit them with some good hard science about the transformer. That’s very often how it happens: hook them with some kind of application, then take them into it conceptually, let them flounder — that’s where I think what the Japanese do is a good idea — let them talk about some of their ideas, then give them an algorithm, a formula and a few examples. Whereas we typically start with the formula with a few sentences about it, and then have them do worksheets.

MPJ: The report states that American textbooks cover too many topics, yet they typically have only fifteen chapters.

Dr. Schmidt: That is mistaking the notion of what a topic is. The definition of topic has to do with the substance of the mathematics, and when we defined it that way, the measurement across all these topics is not how many chapters are in each book.

MPJ: Can you give us an example of four or five topics?

Dr. Schmidt: Congruence and similarity, three-dimensional geometry, linear equations, and fractions. We actually tested 44 topics and determined how many of these topics were in any given textbook. Our 700 page books address about 35 topics. The Japanese, on the other hand, spend half of the eighth grade year on congruence and similarity alone, and their gain in that year is higher than in any other country. The dilemma I have in telling you what to do is that the teacher shouldn’t decide which five to ten topics should be studied in a year. It only works if somebody coherently lays this thing out as to what needs to be done.

MPJ: Do you have any last things to add?

Dr. Schmidt: People still think that there are general things a teacher should do, like cooperative learning. That’s what people push. We push all the things that have nothing to do with subject matter. I’d like to challenge the notion that there is a single way to do things. If you listen to the ideological left, they say that there is only one way to teach. And the data just do not support that. Among the top achieving countries you cannot find one dominate way of teaching. On the other hand, the ideological right are calling for “the basics.” Yet, the latest analysis shows that the United States, through 8th grade, does average or above average in all the standard arithmetic skills. This is not the place were we are hurting the most. That is all we teach. That is what’s wrong, we never go beyond the basics.

If I wanted to become rich and be an advisor to schools to jack their scores up, I know how to do it. We have certain areas of math that we have the international comparisons on. I can tell you the seven items that we are the weakest on, and if schools just did something in those areas, we’d go up in the international rankings. None of those areas is anything that we would consider the basics.

MPJ: What are those area of weakness?

Dr. Schmidt: Measurement, error analysis, geometric shapes, perimeter, area and volume, congruence, similarity, vectors, geometric transformations, and three-dimensional geometry. These are not the basics.

MPJ: Tomorrow, our readers will not be able to change the textbooks or create national standards. What can a teacher do in the classroom today that will model the type of change that you and the TIMSS report call for?

Dr. Schmidt: That’s a tough question, because most of what I have argued is, based on the data, these really are systemic issues. However, the data also shows that how we teach is as important as what we teach. Teachers should challenge students with more mathematical substance and develop the ideas more conceptually rather than algorithmically.

# Stats Are Like A Fist Full Of Worms

Algebra is like an ox. It does a lot of work for us, obeys our commands and remains very predictable.

Geometry is like a puppy. It’s fun to play with, doesn’t ask for anything other than your attention, and doesn’t promise anything other than that in return.

Calculus is like a horse. It is gorgeous to watch when it runs, exhilarating to ride and takes us places we have never been before.

Statistics are like a fist full of worms. They wiggle around and are hard to get a hold of. They live underground, so you always have to dig deep to find them. Once you get one, you don’t know what to do with it other than stick it on a hook and cast it out into the ocean in hopes that it brings you back something useful.

# Get to the Core of The Core

The Common Core curriculum can basically be summed up in the following sentence:

Teach your students to THINK and COMMUNICATE their thinking.

Thinking and communicating are the 21st Century skills. Many people believe that the skills of the future involve the competent use of technology. While it is true that using digital tools in school and the work place is the new reality, it is actually the proliferation of technology that makes thinking and communicating imperative in the information age. When all the knowledge of humankind is available at anyone’s fingertips, memorizing information becomes far less important than being able to construct, evaluate and apply it. You can Google information; you cannot Google thinking.

So the core of the Core truly is Thinking & Communicating.

To make my case for this, I would like to pose that the following equation

6 + 4 + 4 + 8 = 22

6 + 4 + 4 + 8 = 21

Before you start shouting that everything you have read on Facebook about the Common Core is true, let me declare that I am using this equation simply as a teaching device, not a true mathematical statement. You will understand what I mean after I present my evidence.

##### 6 Shifts

Let me start my case that the core of the Core is Thinking & Communicating with the 6 Shifts, which are best represented by the following document found at Engage NY.

In essence, these shifts are redefining rigor. Old school rigor was defined as sitting quietly taking notes, and completing long homework assignments in isolation. The new school definition of rigor envelops the last 4 shifts on the list: Fluency, Deep Understanding, Applications, and Dual Intensity. The rigor is now placed on the students’ minds instead of on their behinds.

The shifts are also calling for balance. Dual Intensity insists on both procedural fluency AND critical thinking by the students at a high level. It is not about dual mediocrity or about throwing the old out for the new, but a rich coupling of both mechanics and problem solving.

Therefore, I make the case that:
6 Shifts = 21st Century Skills,
which are to
Think & Communicate.

##### 4 C’s

Another list that is framing much of the Common Core dialoge is the 4 C’s. Resources for this list can be found at Partnership for 21st Century Learning (p21.org).

These C’s redefine school…

The old school definition: A place where young people go to watch old people work.

The new school definition: A place where old people go to teach young people to think.

… and they redefine learning.

The difference of old school vs new school learning can best be contrasted by the following images of the brain.

The image on the left shows a passive brain that just hangs out as we stuff it with esoteric trivia. The image on the right shows a brain being built, symbolizing its plasticity. We now know that when the brain learns, its neurons make new connection with each other. In other words, learning literally builds the brain. The 4 C’s  claim that this building involves the capacity of the students’ brains to Critically Think, Communicate, Create and Collaborate.

Therefore, I make the case that:
4 C’s = 21st Century Skills
which are to
Think & Communicate.

##### 4 Claims

Smarter Balance creates it’s assessments based on 4 Claims. (I teach in California. PARCC has 4 Claims that closely align to those of SBAC.)

Notice that Claims #2 & 3 are explicitly stated as Thinking & Communicating, which also overlaps with two of the 4 C’s. Mathematical modeling is #4, which will be discussed later. I want to point out here that Claim #1 reinforces our idea of Dual Intensity from the 6 shifts.

There are two important notes for teachers about this first claim. 1) It says Concepts and Procedures, not just procedures. The students need to know the why not just the how. 2) The Procedures alone account for about 30% of the new state tests, so if we continue to teach as has been traditionally done in America, we will fail to prepare our students for the other 70% of the exam which will assess their conceptual understanding as well as their abilities in problem solving, communicating and modeling.

Therefore, I make the case that:
4 Claims = 21st Century Skills
which are to
Think & Communicate.

##### 8 Practices

If you open the Common Core Standards for Mathematics, the first two pages of the beastly document contain a detailed description of the Standards of Mathematical Practice. Then at the beginning of each of the grade level sections for the Standards of Content you will find 8 Practices summarized in the grey box shown below.
What do you notice about the list? Indeed, these habits of mind all involve Thinking & Communicating. While the content standards change with each new grade level, the practice standards do not. With each year of school the students are expected to get better at these 8 Practices. Notice that the first half of the list has already been included in the ones discussed previously: Problem Solving, Communicating Reasoning, Constructing Viable Arguments and Modeling. A case is often made that the other four are embedded in these first four. However one might interpret the list, “Memorize and Regurgitate” is not on there.

Therefore, I make the case that:
8 Practices = 21st Century Skills
which are to
Think & Communicate.

##### The Sum of the Numbers

So, as you can now see, the 6 Shifts, the 4 C’s, the 4 Claims and the 8 Practices are all focused on the 21st Century Skills of Thinking & Communicating. Therefore, I can finally, explain my new equation …

Since,

#### then 6 + 4 + 4 + 8 = 21!

None of these numbers represents a list of content, because the content changes brought on by the Common Core, while significant, are actually no big deal in the long run. A few years from now we won’t remember all the fuss regarding Statistics and Transformations, but we will all spend the rest of our careers learning how to teach kids to Think & Communicate.

I rest my case.

# Interview: Dan Meyer on Using a Ladder to Clear a High Bar

Dan Meyer is as close to a celebrity that a math educator can get. We all owe him a debt of gratitude for making math nerds look cool. He deserves his rock star status because he is an amazing presenter, a thought-provoking writer, and an ingenious creator of math tasks.

Behind all the hype, though, is some serious substance. Dan’s ideas are akin to the spirit of MPJ’s lessons in that they seek to engage students in meaningful mathematics, and aspire to teach them high-level cognitive skills. Dan’s methods, though, have a unique twist that challenges teachers’ thinking. I know he has given me a great deal to think on. I hope he does here for you as well.

MPJ
From what we read on your blog, you are about two things: 3-Act Lessons and the Ladder of Abstraction. Let’s start with 3-Act Lessons. Give us the gist of what they are and why they are an effective tool in teaching math.

Dan Meyer
We make huge promises to kids about the power of math in their world. But then we give them these problems that don’t do justice to that power or to the world they live in. Three-act math uses photos and videos to show students a more faithful reproduction of their world and a more faithful reproduction of the practices of applied mathematicians.

MPJ
MPJ has preached for over a decade the need to have students create their own mathematical models (abstract generalizations). Describe your Ladder of Abstraction and how it applies to teaching mathematics.

Dan Meyer
The process of abstraction is extremely powerful and also not something I understood intuitively until I was a long way out of my secondary math education. Basically, whenever we turn the world into a table or an equation or a graph, we LOSE something. People don’t run at a constant rate. The Earth isn’t a perfect sphere. But we abstract a runner into a linear equation and the Earth into a sphere because those abstractions are perfect ENOUGH to help us answer questions. That’s an important part of modeling. Asking, “Is this model perfect enough?”

MPJ
With so many teachers reliant on teaching from the textbook, do you have any ideas on how to get these practices used more regularly in classrooms?

Dan Meyer
I tell teachers what I tell myself: whatever you’re going to teach today, whether it’s pure math or applied math, make sure students have some NEED for it. A better need than “I don’t want to fail this class.” And I offer them techniques for provoking that need. I also offer teachers a homework assignment, an exercise like push ups, to get better at provoking that kind of need: take a photo or a short video and ask people what questions they have about it, if any. If they don’t have any questions, retake the photo or video in a way that provokes more questions. That homework assignment has been incredibly helpful in my own growth.

MPJ
How well do your theories mesh with what is coming down the pike as the Common Core?

Dan Meyer
The modeling practice of the CCSS gets focused treatment in high school. I encourage all of your readers to study high school modeling (it’s only two pages) and ask themselves, “Are the ‘real-world’ problems I assign preparing students to clear this high bar?” Then Google “three-act math” and see if my work can help.

MPJ
What do you intend to prove with your PhD research?

Dan Meyer
I’d like to understand how any or all of this translates to online education.

# Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers

Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers is being published by fellow math blogger, Sue VanHattum of Math Mama Writes. In her book she “brings together the stories of over thirty authors who share their math enthusiasm with their communities, families, or students. After every chapter is a puzzle, game, or activity to get you and your kids playing with math too.”

Sue was kind enough to include an article I wrote, Textbook Free, as one of the chapters. I am honored to be included in a body of work that is best described by one of the authors as …

a collection of love stories because the authors, including yours truly, want to share something we’re pretty crazy about.  — Fawn Nguyen

In order to raise money for printing costs, Playing With Math has started a crowd-funding campaign. Contributions of any size are welcome, but \$25 gets you a copy of the book. If you are interested in supporting the cause, please visit incite.org.

Sue VanHattum has assembled a marvelously useful and inspiring book. It is filled with stories by people who don’t just love math, they share that love with others through innovative math activities. Playing With Math is perfect for anyone eager to make math absorbing, entertaining, and fun. — Laura Grace Weldon, author of Free Range Learning

Let’s all help Sue make this terrific resource happen!