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.

The Project School Visit

Recently, a group of educators from the Burlington School District visited The Project School in Bloomington, Indiana. This was part of an ongoing partnership with Daniel Baron, one of the school’s founders.

We had three amazing days of quality time with students in classes and meetings with the school staff.

Some takeaways:

School climate matters. When the staff is happy, it shows. Everyone knows it, especially the students, and it creates a healthy, happy, productive learning environment.

Decision-making based on student needs rather than adult needs feels very different. Adults at The Project School have shared core values that guide their decisions. They are flexible, positive, and student-centered. They shift schedules, resources, groups, and plans throughout the year as needs change.

Multi-age classes have many benefits. Observers noticed all students seeming to rise to the level of the oldest students in the class.  We saw a high level of peer support for learning, greater acceptance of differences, and increased self-sufficiency and student leadership.

Having a really great mission and vision matters. Here is theirs. You can read more on their website.

The mission of The Project School is to uncover, recover and discover the unique gifts and talents that each child brings to school every day. Our school works collaboratively with families, community members and social service agencies to solve real problems, as well as to create art for public spaces. Students graduate from The Project School as stewards of the environment with the will, skill, capacity, and knowledge to contribute to the greater good.

The vision of the Project School is to eliminate the predictive value of race, class, gender and special abilities on student success in our school and in our communities, by working together with families and community to ensure each child’s success.

Student voice and choice is critical. A 1st through 8th grade multi-age daily class called Passions helped us see how school can be more enjoyable for everyone.

Themes and big questions are powerful. This year they are focusing on Struggle and Progress.

Problems, Projects, and Place make up the P3 framework used by The Project School. Students do integrated, relevant, compelling projects throughout the year.

Wow! The trip gave me a lot to think about. Our group will continue to meet relative to this experience and our work in Burlington.

Thanks to Daniel and the rest of The Project School staff for helping us see some different ways of thinking about and doing education.

Fix It

I appreciate Marilyn Burns’ presence on Twitter and her blog. She offers great contributions to the math education community.

Marilyn's recent blog post, entitled Fix It: An Activity for Ordering Fractions, is a well-written reflection of a lesson she taught to fifth graders. Marilyn describes how she used an engaging format and includes details of some masterful scaffolding for a student who needed help. It's worth reading the whole thing.

Fix It Fractions reminds me of the Clothesline Fractions activity Rebekah Thomas did with her summer school class. Before class, she’d hang a set of fractions (using clothespins) on a length of string in her classroom. A different student was in charge of “fixing” them each day (putting the fractions in order). The student presented his or her work to the class along with an explanation.

In Marilyn’s activity, students create their own Fix It Fractions sets for others to try.

There is something inherently compelling about fixing. It is different than doing math work that involves simply performing a calculation or solving a problem. Students look at the work of someone else that may be intentionally or unintentionally incorrect and perform an error analysis. There are lots of formats for doing this, including My Favorite No, or presenting two or more solutions and asking students which is correct and why.

I always appreciate when I see error analysis type tasks in Eureka Math lessons, Smarter Balanced Assessments (both of which we use in our district), and other materials. When I think back to different jobs I have held in my life, I think the majority of my time was spent interpreting, analyzing, adapting, correcting, and reimagining work that had been begun by others.

Let’s think about how to include more of this type of approach for students, and see if it improves their school experience.

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?

Geodesic Dome Building, Part I

Ada Leaphart, Integrated Arts Academy Art Teacher Extraordinaire, and I have embarked on an adventure. We’ve got all the fourth graders at IAA building geodesic domes out of newspaper.

I really don’t know how this is going to end up, so that is why I have named this Part I. I hope to report back with more news as the project progresses.

Ada and I decided to keep things loose. We didn’t want to figure everything out for the students by creating our own dome first, learning all the lessons, and then presenting a tidy scenario.

Instead, we have never attempted to create a geodesic dome out of newspaper or anything else, for that matter. Sometimes STEM+Art (I, unlike others, am not wanting to call that STEAM) should be messy and students should have the fun of making mistakes and doing all the figuring.

Before the students got started building, Ada showed a photo of a geodesic dome and asked students what they noticed. We got some math+art conversation going from that, as students noticed many geometric shapes, like triangles, pentagons, hexagons, and trapezoids. Then we talked about old Bucky Fuller (every class asked if he was still living) and how he really wanted to make the world a better place for everyone by using an efficient structure like a dome for shelter.

Kids couldn’t wait to get started. Here are the instructions we are using from PBS.

It turns out, you can roll newspaper in a loose, floppy, weak way or you can roll it in a very tight, very strong roll. Students shared successful and unsuccessful techniques. Among the successful techniques invented by students are 1) Asking someone else to help you tape the roll, 2) asking someone else for help, period, 3) twisting the roll when it is finished to make it even tighter, and 4) using a pencil to act as the center of the roll, then shaking it loose once the roll is finished.

We ended up with enough rolls to make one or two domes. 65 usable rolls are needed. Next time we will need to establish a Quality Control group to assess, select, and count the rolls we’ve got. Ada and I aren’t sure how the whole thing is going to go. At the end of it all I would like to set the dome on fire in the playground. I am not sure we will get permission for that. Oh well, we’re going to roll with it.

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

Keep the Mystery

A few years ago, my husband told me he thought he saw a wolf running across our dirt road. At the time I said no, but maybe he was right. The creature he could have seen is a so-called coywolf, a coyote+wolf+dog that has allegedly established itself in the forests and neighborhoods of New England.

Yesterday, I was reading about the coywolf in the New York Times and was reminded of the incredible nuance, mystery, and ambiguity of the study of genetics and evolution. “Should You Fear the Pizzly Bear?” by Moises Velasquez-Manoff is an article about the effects of climate change on speciation.

“The dirty secret of biology is that the fundamental unit of science - i.e. species - in fact can’t be adequately defined,” said a Monterey Bay Aquarium scientist.

Even Charles Darwin saw the difficulty in the notion of species. From the Velasuez-Manoff article, “...[Darwin] was vague on how to define species, referring to ‘the vain search for the undiscovered and undiscoverable essence of the term.’”

As a child and then a teenager in school, science was presented as something that was unambiguous, and something that smart scientists in labs somewhere were doing with precision and finality. I was shocked when I began studying evolutionary biology in college. The taxonomic system of classification, a construct created by humans, prompted more questions than answers, its tree model seeming too simplistic to adequately explain the breadth and nuance of life on Earth.

Science became interesting to me at that point. I realized that everything wasn’t figured out already and people like me could join the conversation.

My learning about epigenetics in college caused me to question some of what I’d been taught about genes and heredity. Today, there is growing evidence and acceptance of the idea that traits can be inherited that are not written in one’s actual DNA. This directly contradicts what I was taught in high school biology.

As an educator who creates or curates units and lesson plans, often the temptation is to simplify things for students (and teachers). Another temptation is to rely on knowledge of a subject from my own (increasingly distant) school days. Do we present science in all its bizarre, unknowable complexity? How can teachers challenge even young students with unanswerable questions?

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!

Helping students doesn't mean showing them how

A few days ago, I was in a professional development meeting with paraeducators at C.P. Smith Elementary School. We were discussing how best to help students in math. We had a great conversation about it and talked about the idea of asking instead of telling. Our focus was #1 and #3 of the eight Common Core Math Practice Standards. I’d printed some questions that I have seen on several different websites, so I am not sure of the original author. Here they are:

Make sense of problems and persevere in solving them

• How would you describe the problem in your own words?
• How would you describe what you are trying to find?
• What do you notice about...?
• What information is given in the problem?
• Describe the relationship between the quantities.
• Describe what you have already tried. What might you change?
• Talk me through the steps you’ve used to this point.
• What steps in the process are you most confident about?
• What are some other strategies you might try?
• What are some other problems that are similar to this one?
• How might you use one of your previous problems to help you begin?
• How else might you organize...represent... show...?

Construct viable arguments and critique the reasoning of others.

• What mathematical evidence would support your solution?
• How can we be sure that...? / How could you prove that...?
• Will it still work if...?
• What were you considering when...?
• How did you decide to try that strategy?
• How did you test whether your approach worked?
• How did you decide what the problem was asking you to find? (What was unknown?)
• Did you try a method that did not work? Why didn’t it work? Would it ever work? Why or why not?
• What is the same and what is different about...?
• How could you demonstrate a counter-example?

After the paraeducator meeting, I came across an Edutopia article entitled, “Takeaways from Math Methods: How will you teach effectively?” It is about pre-service teachers who have taken a math course. This jumped out at me.

Helping Students Doesn't Mean Showing Them How

Before admitting [preservice teachers], we interview each one and ask, "Why do you want to be a teacher?" The most common response is, "I want to help students," a sentiment that PSTs describe later as "giving good explanations" or "making it simpler" -- notions of helping which are underdeveloped.

A synthesis of research in mathematics education by James Hiebert and Douglas Grouws identified two teacher actions that impact conceptual understanding. One is to engage students in productive struggle. Merely telling students how or making things simpler does not actually help them understand as much as providing challenging tasks and time to "dig in" to a problem.

To help them redefine how to help students learn, I encourage [teachers] to embrace their sense of accomplishment when they solve a challenging task, recognize the pride they feel when they share a unique way to solve a problem, and reflect on what such feelings might mean for a student in their own classroom.

The way this piece is written states an important idea in a concise, clear way. I hope to keep pushing myself and others to ask, watch, and listen instead of show and tell.

Hour of Code Video

This was so much fun!

What Google has learned about hiring

A few days ago, the New York Times published an interview by Adam Bryant entitled “In Head-Hunting, Big Data May Not Be Such a Big Deal”. Bryant interviewed Lazslo Bock, a Google executive, about what Google has learned about what works and what doesn’t when it comes to hiring new employees.

Google has the resources to crunch numbers on employee performance or success and match that to hiring criteria. Most of the rest of us don’t, so this is worth reading. Here are a few things that stood out for me, as someone who participates on hiring committees and tends to wonder how good I am at judging applicants.

“Years ago, we did a study to determine whether anyone at Google is particularly good at hiring. We looked at tens of thousands of interviews, and everyone who had done the interviews and what they scored the candidate, and how that person ultimately performed in their job. We found zero relationship.”

“On the hiring side, we found that brainteasers are a complete waste of time...What works well are structured behavioral interviews, where you have a consistent rubric for how you assess people, rather than having each interviewer just make stuff up...[also] where you’re not giving someone a hypothetical, but you’re starting with a question like, “Give me an example of a time when you solved an analytically difficult problem.”

“Twice a year, anybody who has a manager is surveyed on the manager’s qualities...We then share that with the manager, and we track improvement across the whole company. Over the last three years, we’ve significantly improved the quality of people management at Google, measured by how happy people are with their managers...for most [managers], just knowing that information causes them to change their conduct.”

Lastly, this is my favorite bit from the article:

“...G.P.A.’s are worthless as a criteria for hiring, and test scores are worthless...We found that they don’t predict anything...the proportion of people without any college education at Google has increased over time...academic environments are artificial environments. People who succeed there are...conditioned to succeed in that environment. One of my own frustrations when I was in college and grad school is that you knew the professor was looking for a specific answer...You want people who like figuring out stuff where there is no obvious answer.”

These insights have far-reaching implications for teachers, not just members of hiring committees.