NCSM Boston, 2015. Monday

A room full of math coaches! 

NCSM Boston. Some of my Monday notes.

Jo Boaler’s Keynote

On teacher attitudes

We urgently need to shift teachers, parents, and students ideas about who can achieve in mathematics.

Students of color and girls show the sharpest increase in achievement with mindset interventions.

On achievement

The lowest achievers in the world are the "memorizers".

The highest achievers in the world are those who think about big ideas and connections.

On mistakes

Every time you make a mistake in math a synapse fires. When you get a question correct, there is no brain growth.

Teachers should encourage mistakes.

Students need open and challenging work so they will make mistakes.

Teachers need to change classroom culture to openly value mistakes.

Jo has a new version of her book, called What’s Math Got To Do With It

Jo is working on a Week of Inspirational Math, a series of free lessons designed to be used for the first week of school.

Susan Jo Russell

How "Lingering" on Ideas about the Meaning of the Operations Can Include All Students in Significant Learning

Access and equity

Engaging students with challenging tasks, discourse, and open-ended problem solving has the potential to raise the mathematics achievement of all students, including poor and low income students.

"Productive lingering" is essential to engaging in mathematical argument for all.

Amy Lucenta, Grace Kelemanik, Susan Creighton

Engaging ALL Learners in Mathematical Practices through Instructional Routines

All students must be able to…

Interpret and chunk complicated objects,

connect representations

change the form of the numbers, expressions, space, etc. to create and leverage equivalences,

recall and use properties, rules of operations and geometric relationships,

and find the right distance from a problem...i.e. shift perspective.

The math practices open doors for struggling students.

Problems were presented and the audience was asked what we noticed. We were encouraged to find “shortcuts”. However, the shortcuts are based on mathematical reasoning, and are one way to facilitate productive math classes.

If we don't seal the deal with a meta-reflection, we are just talking about strategies.

Students generate “Ask Myself” questions.

Next time I will ....before I calculate because....

Paying attention to ....is helpful because....

Deborah Ball, et al

How can explicitness about mathematical practices support equitable instruction?

Deborah Ball teaching video

Task: Make as many 3 digit numbers as possible using the digits 4, 5, and 6.

I would like someone to give a wrong answer to this problem.

Do others agree this is wrong?

Can someone share one reason why it is not one of the answers?

Explicit teaching…

… unpacks practices or knowledge to make it open to learners, not doing it for them.

...is not about the teacher demonstrating.

...seeks to maintain complexity but make complex practice accessible to all students.

Students do the work, teacher highlights what they just did. Makes elements visible, provides language and supports.

I have opinions about the idea that “mathematicians are lazy” and the term “shortcuts”. I won’t share those now, nor will I write about more speakers I saw on Monday, or all the other questions and thoughts I have, because I am tired and have to get to sleep. Another time.

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.

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.

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.

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?

Organizing Information

New York Public Library

Max Ray’s talk at NCSM was about a math lesson he taught twice. The first time things didn’t go as well as he’d hoped. Max had the opportunity to reflect with his collaborators afterward. Luckily, they were going to teach the same lesson again to another group of students the same day. They decided what they wanted to do differently based on the results from the first group.

Here is the excellent write-up of that lesson by Max. The second go at the lesson is one in which the teachers respond to students who need support by modeling an organizational strategy. They actively avoid giving students hints about how they might mathematize the problem situation they’ve been given. It is no surprise that Max has done a nice job organizing the student-teacher-student volley into tables in his article. The outcomes in the second lesson are superior.

The ability to organize information is an important skill. When I observe students engaging in math problem-solving, often their success hinges on if and how they organize their work. Organizing information is also the key to great writing, troubleshooting, designing websites and databases, waiting tables, using spreadsheets, teaching, talking, and many other things. Here is Rob Lamb’s Collaborative Infographics for Science Literacy site, which also relates.

If you are a teacher, test it. See how students respond if you honor their ideas and teach only organizational strategies.

NOLA Greats

There is a treasure trove of greatness at NCSM New Orleans. See below for conference tweets that will link you to wonderful minds and resources.

Choose a problem and anticipate student responses. T/F: 80/4=(80/2)+(80/2). Kazemi & Hintz

Rethink homework! Purpose is not to give a child a grade, ever. What's your homework protocol? @tkanold tkanold.blogspot.com

Go beyond checking for understanding. Students must get feedback, take action. @tkanold

Working on our practice. Teach the same lesson twice with collaborative reflection in between. Nice! @maxmathforum http://mathforum.org/pps/

Number sense is acquired; you don't teach it, you nurture its development. @SkipFennell mathspecialists.org

Set it up so kids are asking the next question of the teacher, using the lang. of our discipline. @jgough http://jplgough.wordpress.com/

Stop making excuses. Implement what we know works. @steve_leinwand http://steveleinwand.com/

We say all students can learn, now we need to act that way. Cathy Seeley (via @Maryvfitz)

Connie Knodt and Grit

My friend Suzy texted me last week to tell me she was listening to a wonderful piece on NPR’s TED Radio Hour about “grit”. Here’s the link to the story, entitled Is Having Grit the Key to Success?
The concept of grit or perseverance keeps coming up in my work, because the first math practice standard in the Common Core is “Make sense of problems and persevere in solving them”...and, more importantly, because teachers and parents know that determination and the ability to cope with failure is paramount to student success.
Last night I had the pleasure of speaking with Connie Knodt, a relatively new member of my family. She was featured recently on WCAX’s Super Senior series. Connie is 79 years old and still works 28 hours a week at Fletcher Allen Hospital in the pediatric ward. Here’s the link to her story. Connie and I had a great conversation about how she was able to transcend a difficult childhood to become an IBM engineer when few women did such a thing. I asked if she could remember anyone who was an important role model for her when she was young. Without hesitating, she told me about two top-notch high school teachers who inspired her to become to lifelong learner she is today. She remembered their names and talked in detail about how her geometry teacher asked the students to build structures rather than assigning pages in a textbook.
Connie’s story reminds us that teachers are so important. One great teacher can turn a life around.
Connie is also a living testament to grit. She’s interested in solving tough problems and never being finished with her own learning. She told me that at work if there’s a new computer system, medical device, or scheduling conundrum, they bring it to her. She’s happy to take on the challenge.

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.