Space for All Learners

In my ongoing quest to find great math resources on Twitter (not hard), I started following Steve Wyborney (@SteveWyborney). Steve is a math teacher and coach in Oregon. He has been posting high quality math activities immediately usable by elementary teachers. I will share a few of them here.

Teachers often struggle with math tasks that feel just right for some students but not others. Steve’s activities are accessible by a wide range of learners in the elementary grades. They provide access points for many but also opportunities for challenge within the realm of grade-appropriate number sense, place value understanding, and additive or multiplicative reasoning.

Provide Massive Space to Notice

Steve has created this subitizing/number patterns video that teachers can show to students, pausing at a certain spot to allow thinking and noticing. It couldn’t be much easier. He provides a printable page to give to students. Simple to try, powerful results.

The Maze Hundreds Chart

Watch Steve’s video of ideas for how to use this resource. Then you can get the interactive powerpoint slide he created and try it with students. I can’t get it to work on a Chromebook, so you probably need a computer with Powerpoint installed.

Also try The Green Light Hundreds Chart and The Animated Multiplication Table.

These are simple tools, already frequently used in elementary mathematics, but often without the kind of exploration and reflection encouraged by Steve.

If you explore Steve’s blog, I’m on a Learning Mission, you will find lots more high quality instructional strategies as well as tools that are immediately usable with students.

If I Had a Hammer

Peter, Paul & Mary

I just read a great blog post by Tracy Zager. Her blog is called Becoming the Math Teacher You Wish You’d Had.

It is about getting students out of the normal (sometimes boring) routines they’ve become accustomed to in math class.

Tracy describes being in a workshop with Brian Hopkins and doing a bunch of math problems in groups. Her group solved a problem and then there was discussion and learning about the mathematics that best fit that problem. When Brian posed a seemingly similar problem, Tracy assumed they would be applying that same mathematical construct to the new problem. That was not the case, which surprised Tracy.

“...Brian disrupted the predictable, pitter-pat routine of math class...

What I see in schools is we cue kids to know what tool to use. If we’re two weeks into a unit on fractions and we give them a story problem, the kids figure fractions are involved. If the name of the chapter is “Multiplying Two-Digit Numbers” and it’s written on the bottom of the worksheet, the kids are going to assume they should multiply some 2-digit numbers. If we’ve written an objective about linear equations on the board, kids figure the answer is going to involve linear equations. If my new tool is the hammer that divides fractions, I’m going to use that hammer until my teacher tells me it’s time to switch hammers.”

As educators, we are often frustrated by our students’ lack of ability to make sense of and solve problems (the first Common Core math practice standard). Yet, are we giving students experiences in math class that help or hinder their ability to solve problems?

Student Self-Assessment

I want to send a huge shout out to Bill Ferriter, here in Burlington from Raleigh, North Carolina. Bill is a sixth grade science teacher with a year-round school schedule that allows him to visit us during our academic year. He is helping Burlington educators improve our collaborative process and our work with students.

One of my big takeaways from spending time with Bill is the importance of student self-assessment. Teaching teams in Burlington have begun creating unit overviews which are given to students so they can chart their learning. Unit overviews vary depending on the teachers and grade level, but most have a way for students to indicate what they know and can do relative to important learning targets. Older students might make a mark on a line somewhere between “Not Yet” and “Got It”, while younger students color in a box or a smiley face next to a skill they have mastered. More important than the format is the fact that students work on their awareness of their own learning. They begin to take responsibility for assessing themselves, rather than leaving that up to parents and teachers.

Researchers and thought leaders in education from Marzano to Wiggins to Hattie agree -- students who are aware of their learning objectives and who are responsible for assessing, charting and sharing their own progress are more likely to be successful. Yet, according to Bill and others, students are rarely asked to assess themselves.

I have been studying the Common Core Standards for years, especially in math at the elementary level, and I think they are mostly wonderful. The content standards emphasize conceptual understanding and depth over breadth. The practice standards focus on critical skills like problem-solving, constructing viable arguments, and critiquing the reasoning of others. An activity like problem-solving requires a good deal of self-awareness and the ability to “...monitor and evaluate their progress and change course if necessary” (a direct quote from the CCSSM). So, in order to master the standards, students would need to have a measure of meta-cognition. However, student self-assessment is not an explicit part of the standards, nor is it an obvious feature in a Common Core program like Eureka Math (EngageNY).

So, how do we ensure students are responsible for self-assessment if it doesn't appear in the standards and programs? Using unit overviews is one way. When a PLC  team creates a unit overview, they have the opportunity to collaboratively determine the most important learning targets for their students. In doing so, they have also created a product that students can use to know their goals and take charge of their learning.

STEM and Equity in the Burlington School District

I am enough of an artist to draw freely upon my imagination. Imagination is more important than knowledge. Knowledge is limited. Imagination encircles the world.

― Albert Einstein

Recently, a budget draft included funding of a STEM position at Flynn Elementary. Here is why adding and/or strengthening STEM education at Flynn and in all Burlington schools is the right thing to do.

STEM is cutting edge education.

STEM stands for Science, Technology, Engineering and Mathematics. At its best STEM education consists of hands-on, student-centered design challenges and project-based learning that cultivates the imagination.

Einstein’s remarks about the importance of imagination have never been more apt.

The world is changing so rapidly that no one can anticipate what, specifically, students will need to know. We must equip them for success in a in a technology-driven world that demands continual learning. Students should be offered broad and varied opportunities to take charge of their own education, collaborate, communicate, design and synthesize.

STEM is diversity and equity.

Quality STEM education is enemy of the achievement gap. Women and people of color are still underrepresented in STEM classes in high schools, STEM majors in college, and STEM fields in the workforce. Women and people of color are equally capable of excelling in this work and they provide much-needed perspectives. We have to ask why the demographics of these fields continue to be skewed. The fact is that we still live in a world full of biases and systemic discrimination. Education is a critical part of the solution. Stereotypes, biases and barriers don’t go away without concerted effort to counteract them.

The importance of high quality STEM education goes beyond giving students opportunities in STEM fields. It makes school a place where more students are able to be successful, period. Hands-on, student-centered design challenges, a hallmark of STEM, tend to work better for all students than traditional pedagogy. Students who are from low income families, are non-white, are new Americans and/or English language learners are at greater risk for under performance in school. STEM helps these students. Education for equity means providing engaging, challenging work for all students.

As a K-5 Math Coach in the Burlington School District, I have personally witnessed the power of STEM education. Individuals who are less successful in traditional learning situations shine when engaged in high quality STEM learning opportunities. I’ve watched students who typically exhibit challenging behaviors and low academic performance become energized about computer programming, exploring fractals in art and nature, catapult building, geodesic dome construction, and on and on. It is hard not to become an advocate of this type of education after watching marginalized students get opportunities to demonstrate their brilliance.

STEM is for Burlington

It is wise to fund STEM education in Burlington. By investing in STEM, we are focusing on what really works for achievement and equity. This is a forward-thinking opportunity to empower our students to be the leaders, thinkers, and makers of a changing world. Imagine that.

Vermont Fest 2014 and a Snake

The sign of a good conference is when you come away from it questioning everything about your work.

I like this snake drawing from the New York Public Library more than the three terrible photos I took of people in banquet rooms at the Killington Grand. I would never consider publishing a blog post without a picture.

At Vermont Fest this year, I found myself wanting to make a list of a bunch of things all students should get the chance to do in school.

Skype/hangout/video interact with people in other parts of the world

Type an equal sign into a spreadsheet

Make a personalized, LED-lit badge to explore how light works

Have maker/genius/whatever hour/day/week to explore something interesting to them

Publish their content (writing/photos/videos) on a blog and comment on the work of others

Learn about how computers work by writing some code

Be asked the questions How are you feeling? What do you think? and What do you need?

Use Google Research Tools to find and cite things.

Sit in chairs listening to a teacher talk a lot less.

Some great presenters I encountered include Chris Lehmann (@chrislehmann), Bonnie Birdsall (@bonniebird), Dan French (@danfrench), Adam Provost (@batman44), Lucie deLaBruere (@techsavvygirl), Charlie Macfadyen (@csmacf), Tricia Hinkle (@VTScienceFair), Matt Dunne (@@mattdunnevt). Check them out.

Here are a couple of links.

Using Google Sheets in the Classroom

Tricia Hinkle’s site

Bonnie Birdsall’s writing tech site

The Vermont Fest site with all kinds of other links to presenters

Fibonacci and Fractals Links

I had the pleasure of being the co-presenter of a workshop called “Fibonacci, Fractals, and the Common Core Math Standards” at the VCTM conference at Saint Michael’s College on Friday. My partners were Professor Tim Whiteford of Saint Michael’s College and Laura Sommariva, a math teacher at Colchester High School.

The three of us shared what we’d done with students during a fifth grade field trip to Tim’s famous Penny Arcade. Here is Tim’s original write-up about that.

As promised, for the participants in our workshop and others, here are the resources we used to teach about fractals and Fibonacci numbers.

The Fractal Foundation Fractivities. How to draw Sierpinski triangles, do fractal cutouts and more.

Worksheetworks. Create your own graph paper and triangle paper.

On Being a Plant, Part 1, the 6 minute Vi Hart video we watched. She explains Fibonacci numbers, and demonstrates how to count the spirals on pinecones, draw realistic pinecones, and use graph paper to make a golden spiral.

Laura teaches summer math classes for elementary students in Switzerland. She has photos of her students here doing wonderful, related activities like building giant tetrahedrons out of mini marshmallows.

Have fun!

Shelburne Farms Mini Maker Faire

I went to the Maker Faire at Shelburne Farms today for the first time.

This is what I did.

I made a magic wand with an LED light that turns on and off by touching a wire to a battery on the wand. I first had to figure out how to connect the LED to some wires, then run them to the battery correctly. After that part was working, I added sparkly silver ribbon to the stem of the wand and encased the LED light in crumply clear plastic tape for light refraction purposes. Voila! I am ready to put spells on people. Joanna Elliott, Flynn Elementary parent and teacher, was the wizard behind this project. See her fabulous art blog.

I made a puzzle book, a square flexagon (a previously unknown-to-me relative of the hexaflexagon) for comic-book type story-telling, and a mini book that could contain anything from math facts to the secrets of the universe. A matchbook size mini book can be made and then kept in an actual matchbox. Book Arts Guild of Vermont people helped me do this. Students might want to make these after reading the Red Clover Book entitled The Matchbox Diary by Paul Fleischman. This is an activity for any budget.

I spoke with Richa, who is going to assist with a course called Intro to Relational Databases at Girl Develop It Burlington. There are classes and meet-ups. I want to go.

Champlain College Emergent Media Center folks explained what they are working on. Their new Maker Lab that had its grand opening party last night.

I saw a robot-building challenge and presentation by Joe Chase and his team of students from Essex High School. Joe is my neighbor and it was great to see him up there advocating for more design and engineering work in schools. My daughter took his robotics class a few years ago and loved it.

I saw and did many other cool things, including experimenting with magnets with Frank White from CreateItLab and speaking with the effervescent Michael Metz of Generator, Lucy deLaBruere, Courtney Asaro, and Graham Clarke, both of Flynn Elementary School in Burlington.

What a great day! Takeaways included an Arduino Robot Kit made by YourDuino.com and the knowledge that so many people are working on creating engaging opportunities for people of all ages in the Burlington area.

Summer Gems

Here are two articles you shouldn’t miss this summer, and they make a nice pair.

“Why Do Americans Stink at Math?” by Elizabeth Green, July 23, New York Times, and “Most Math Problems Do Not Have a Unique Right Answer” by Keith Devlin, August 1, 2014, Devlin’s Angle.

I’ve come to the conclusion that our old ideas and stereotypes about math and education are hard to shake. It really means reading articles like these as they come out every month or so, in order to truly change our minds and our practice.

To whet your appetite, here are a few quotes:

One of the first math classes he observed gave him such a jolt that he assumed there must have been some kind of mistake. The class looked exactly like his own memories of school. “I thought, Well, that’s only this class,” Takahashi said. But the next class looked like the first, and so did the next and the one after that. The Americans might have invented the world’s best methods for teaching math to children, but it was difficult to find anyone actually using them. - from “Why Do Americans Stink at Math?”

Having earned my living as a mathematician for over 40 years, I can assure you that the belief is false. In addition to my university research, I have done mathematical work for the U. S. Intelligence Community, the U.S. Army, private defense contractors, and a number of for-profit companies. In not one of those projects was I paid to find "the right answer." No one thought for one moment that there could be such a thing. - from “Most Math Problems Do Not Have a Unique Right Answer”

The last summer gem is this youcubed video about using Number Talks in math class. How would you solve 18 x 5 mentally?

Hit the Target

I was fortunate that my boss found out about a STEM (Science + Technology + Engineering + Math) Coaches course taught by Dr. John Tapper and registered me and our district science coach. We spent four whole days at the Hampton Inn, which is a strange venue for a STEM course but it worked fine. I gained about 5 pounds because the hotel served muffins every morning and cookies every afternoon and I ate them.

I already knew John Tapper from afar because of his excellent book on math instruction called Solving for Why. This course wasn’t about math menus and differentiation; instead John got us thinking about teaching STEM and instructional coaching. There was lots of discussion, not lots of lecturing, and plenty of hands-on investigations involving buoyancy, force, and motion. John teaches college level math and education courses, but has experience as an elementary classroom teacher, administrator, instructional coach and researcher. I found his perspective refreshing and some of his ideas about STEM new to me.

I’d been wondering how to best integrate math with other content areas. In the STEM Coaches course, John pushed us to use math in a meaningful way rather than as an add-on. He asked, “What about challenging students to create a mathematical model that they will then use to make a prediction?”

It turns out there are fun, engaging ways to do just that. John gave us Straw Rocket Launchers (go here if you want plans to make your own). Two teams experimented with these, adjusting the launch angle and launch force to see how to get the straw to travel different distances. When each team felt they had enough data, John placed a hotel napkin on the sidewalk. “It must hit this target!” Teams measured the distance to the target, then decided how to set the angle and force of the launcher. No more practice runs - each team had one chance to get it right. See photos below of classmates crunching the numbers, then trying to hit the square.

There were a few different targets. Both teams were able to hit the napkin, but the small soup cup John put out was too tough.

It helped to experience these challenges as a learner. Everyone was engaged in the task and we had to really use the math and rely on it to be successful. A key point: hitting a target at a given (initially unknown) distance is very different than simply sending a rocket as far as it can go. The math ended up being the centerpiece of the activity, and the whole thing was really FUN.

We also tried to determine the minimum surface area for an effective parachute, create our own timer (pendulums, a hole in a water bottle), and decide how to predict if a given object would sink or float.

I have a new sense of how to use all four letters in STEM in a meaningful way, and how to give students greater ownership of their learning.

We should all try to hit the target!

B Positive

B Positive is my blood type, and it has served as an important reminder about my attitude toward all things work-related (and non work-related).

I attended Dynamic Landscapes last week at Champlain College and had a wonderful time. The best presenters are those who are super enthusiastic about education and its potential. Though cynical about the way things are, wonderful speakers like Gary Stager, Thursday’s keynote, has an optimistic vision.

Gary says...

I am not surprised when kids do extraordinary things. I am surprised when adults are surprised when kids do extraordinary things.

What are kids really capable of? We need to find out.

Gary Stager is worth getting to know if you are an educator. He’s an advocate for kids working to their fullest potential with technology, and having high/low tech maker spaces in classrooms. His book is called Invent to Learn. Gary makes me want to be more radical.

At Dynamic Landscapes, I also attended a panel of educators who recently hosted the Smarter Balanced Assessment (Common Core) field test in their schools, facilitated by Peter Drescher of the Vermont Agency of Education. My district isn’t part of the field test, so it was great to hear from folks who know more. There was discussion of the nuts and bolts of the new assessment like the fact that students could take the test on a tablet but are supposed to have an external keyboard. There was talk of how to schedule the test to make it work, how to test the wireless capacity of the schools, how to prepare students and teachers.

I noticed that many of the educators who have administered the Smarter Balanced field test to students remarked that students enjoyed it. They like the tech format rather than dealing with pencil and paper, they liked the multimedia content, and the challenging questions.

A principal in the audience spoke up. I didn’t know him and didn’t catch his name. He said attitude is everything. This is a positive opportunity to learn. Let’s pull our sleeves up and make this work. There will be challenges, but we will learn a lot. Like any new thing there will be bumps in the road. His positive attitude was adopted by his staff and students.  

There is and will be lots of complaining about the Smarter Balanced assessments. Adult negativity is quickly taken up by students, and could rob them of important opportunities. As a math coach, I will model positivism.

B Positive.

Latest and Greatest in a Nutshell

Dan Meyer

There are some very good things happening right now in the world of mathematics education. Being at the NCSM Conference gave me the opportunity to connect with many of the greatest minds in the field and hear about their current projects.

Here are my top picks for books to buy, courses to take, blogs to read...right NOW.

Books

NCTM’s Principles to Actions: Ensuring Mathematical Success for All. The book Steve Leinwand keeps waving around. I read a draft in the fall. Educators need to start turning to this when figuring out how to do professional development, how to craft school goals, what to look for in classrooms. It’s radical.

Visible Learning by John Hattie. This book is being enthusiastically talked about by greats like Tim Kanold and Bob Laird. Subtitled “A Synthesis of Over 800 Meta-Analyses Relating to Achievement”, it’s the new go-to resource for knowing what truly works in education.

Smarter Together: Collaboration and Equity in the Elementary Math Classroom by Featherstone, et al.

Blogs

Tim Kanold. Check out his most recent post about math homework.

Max Ray. I went to an excellent workshop for teachers by Max and also saw his engaging Ignite talk. He’s with the Math Forum @ Drexel. There are problems, videos and more.

Dan Meyer. Prolific blogger, thinker. Recently published Great Modeling Tasks in Three Acts (for NCSM members only, except for one freebie).

Annie Fetter. At Math Forum with Max. Great Ignite talk about her artist mother and the math she used.

YouCubed. Not a blog but go there and sign up for updates. Watch some of the videos.

Courses

There are two online Stanford courses taught by Jo Boaler that are a must-do. Last summer, I took How to Learn Math for Parents and Teachers. It was fabulous. It was free then, now it costs $125. Worth it.

This year, Jo Boaler has added a brand new course called How to Learn Math for Students. It’s free. I haven’t taken it yet but I recommend trying it with a young person you know. It sounds like it is appropriate for children ages 10-18, but for children younger than 13, a parent or teacher should register and share the material with the child. Go to the site and register. It begins in May.

People to Follow on Twitter

@jgough, @steve_leinwand , @SkipFennell, @maxmathforum, @tkanold, @MFAnnie, @TuvaLabs,@Trianglemancsd, @wahedahbug, @lambchop1998 (I met this guy at NSTA Boston, but he was great), @IllustrateMath, @joboaler

Who I missed

Uri Treisman. But here’s the audio of his talk.