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?

On Productive Failure

Here is a 7 minute video of a young math major, Elly Schofield. She reflects on her K-12 mathematics education, and the disconnect between that and the mathematics she encountered in college.

Educon 2015

I can see why many Educon attendees remarked that they’d spent their own money to be there. The conference, held at Science Leadership Academy in Philadelphia is that good. It was an eclectic group of out-of-the-box thinkers, innovators, and activists. I knew I wanted to go when I saw Chris Lehmann, founding principal of the SLA, speak in Killington last year.

I was a first-timer. Day one was spent at the school - a public high school that is an inquiry-driven, project school - in partnership with the Franklin Institute. I and a few of my colleagues found a student to guide us. She patiently walked us to different classes where we watched, listened, and sat with students to chat. Students in one class passionately explained a project in which they protested the closing of a huge number of Philadelphia public schools. Students in Doug Herman’s photography class told me what they’d learned about composition and layering and why they were in the photography room even though it was actually their lunchtime. In Algebra II they had designed a catapult to hit a target and were typing a reflection about their group process. I was hooked.

Then, of course, there were many great workshops, Ignite talks, and side conversations on Saturday and Sunday. Here are some of the people I met and learned from, along with some quotes and resources.

A highlight of the conference for me and many others, I’m sure, was Raghava KK, the effervescent, charming presenter and self-proclaimed TED whore. Here’s a 4 minute TED on bias and perspectives in history. He helped me remember what it means to be truly creative. You don’t matter, he said to all the educators in the room. Art should be the medium by which stem is taught... Art is how you teach everything... Incorporate visual literacy in everything you do.

Every disagreement is a chance to learn about a different perspective.

Raghava’s co-presenter, Meenoo Rami, an SLA teacher, hosted this session in her classroom. After meeting her, I was sorry I hadn’t made it to her class on Friday.

Diana Laufenberg, of SLA, led a workshop on school transformation and Joni and I sat with a Eric Dale from the Dwight School in NYC and Andrew Gallagher of the NYC Department of Education. We enjoyed hearing about Eric and Andrew's work, marveling over the vastness of the NYC school system. Diana recommended the book Immunity to Change.

Deterritorialize departments. Get away from content and move to skills.

Jamie Gravell shared a collection of articles on Inequity in Education.

The one thing I wish I'd known about was this idea of transformational resistance.

Is the student trying to transform the environment in some way instead of doing something wrong?

Math and Social Justice, was a session I didn’t attend, but wanted to. Thank you for posting these resources.

Burlington High School (Massachusetts) has a course called Help Desk. See their great website here, which was presented by female STEM enthusiasts on their way to becoming engineers.

There was a really cool panel I was late for. I liked the conversation that was happening when I arrived, which included comments from Otis Hackney, Principal of South Philadelphia High School.

When people say ‘they don't have the background knowledge’, I say, it is your job to give them the background knowledge they need! If they walked in already knowing everything, they don't need us. As an educator you have a job to do.

What if you had a school with mostly white students and all black teachers, what would that be like?

David Jakes, Imagining Digital Spaces for Learning. In groups, we designed a digital learning space, but we were not allowed to discuss any specific tools. Anyone who is working in or redesigning a school should read Toolkit for Designing a Digital Atelier.

Have you intentionally designed a space that intentionally supports your vision of learning?

How do you design a physical space for an increasingly virtual education?

Last but not least, I was in a wonderful session called Shifting the Focus: Elevating Student Voices led by students and their teachers, Josh Block and Amal Giknis. First, the students shared their projects and then we were asked to create an “education manifesto” in 30 minutes that could be posted to twitter with hashtag #focusonvoice. The students were so open and passionate in their presentations and then were so effective as they came around to help us with our assignment...this session is one that has really stuck with me. I was fortunate enough to sit with Renee Hawkins, a very thoughtful educator from a school in Baltimore.

I don’t know how I’ll stay away from Educon next year. I had my mind blown by great thinkers, got to spend time with beloved colleagues, and had my first taste of a grapefruit brulee doughnut from Federal Donuts. As Raghava said, Don’t mess with passion.

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.

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.

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.

Letting Go

By Mica Angela Hendricks and daughter

My dear friend, Rachel Wynne, kindly emailed me the link I am about to share. It’s a blog post called “Collaborating with a Four-Year Old”. I just love it. It’s about a mom and her young daughter creating artwork together. The pictures are priceless, and the ideas about sharing and collaboration are profound.

“Those things you hold so dear cannot change and grow and expand unless you loosen your grip on them a little.” - Mica Angela Hendricks, The Busy Mockingbird

St. Louis STEM Reader

I attended the NSTA STEM Conference in St. Louis last week with several colleagues. It was a very worthwhile trip.

Top Quotes

“Engineering naturally integrates mathematics, science, social studies and language literacy.” - Tamara Moore

“Tell kids they are doing engineering. Use that word. Students, especially girls, tend to go to medical school or major in science in college if they enjoy STEM. Very few choose engineering because they don't know what that means.” - Liz Parry

“If you are not iterating, it is not engineering.” - Ann McMahon

“Is it really STEM or is it just John Dewey?” - Tara Bell

Top Takeaways

1. High-quality STEM education is more about the how than the what. We can’t teach students everything they will need to know. We can help them learn how to learn.

2. The habits of mind related to engineering can be a thread running through all content areas. Empathy, collaboration, failure, iteration, perseverance, social justice, activism, leadership.

3. STEM has the potential to make a real difference for equity and diversity. It has been shown to be an effective way to engage struggling or at risk students. Currently, success in STEM subjects in school and in careers is very skewed toward certain demographic groups, and something needs to be done to change that.

Favorite Presenters

Tara Bell, STEM coach at Washington STEM Academy in Champaign, IL

Bob Goodman (New Jersey Center for Teaching and Learning: Ridgewood, NJ) Demystifying Science with the Progressive Science Initiative (PSI) Equity requires that all high school students learn physics, chemistry, and biology. PSI is a free open-source program that is helping schools achieve that goal.

Liz Parry, Coordinator, STEM Partnership Development, The Engineering Place, College of Engineering, NC State University

Ann P. McMahon Ex-Aerospace engineer. Strategies for integrating STEM with social and emotional learning. Ann recently gave a TEDx talked titled Engineering Empathy (use password tedxgladstone).

Beth Bender, Principal of Gateway STEM High School, St. Louis. A public magnet school, 85% FRL, 55% African american, increasing ELL. There is a lack of awareness about engineering, and it is mostly male. Engineering students give demonstrations for other students during lunch; recruiting for the high school is done with hands-on tasks, live puppies.

Tamara Moore, University of Minnesota. STEM Education Center. Said she would soon be running a pilot program of K-6 STEM integrated units that include a heavy children’s literature component.

Resources

Family Engineering (book and website recommended by Liz Parry)

TeachEngineering

Ideo and the Design Thinking for Educators toolkit

New Jersey Center for Teaching and Learning

eGFI

Gateway STEM High School

The Deep Dive

EnLIST Entrepreneurial Leadership in STEM Teaching and Learning

University of Minnesota STEM Education Center

TryEngineering

National Center for Universal Design on Learning

The Future of STEM Education

Hear Professor Roni Ellington’s inspirational talk from TEDxBaltimore, 2013.

Marjorie on Math Munch

There’s a great blog called Math Munch. I mentioned it in a previous post, but I have to revisit it here. I’ve signed up to receive new posts from Math Munch via email, something I don’t usually do. But I’ve found that this is worth the space in my inbox. Each post has a few different topics, everything from cool paper folding projects to high quality videos and online games. You must check it out!

The current Math Munch post includes a piece about a woman named Marjorie Rice who became interested in tesselations and discovered some new ones on her own. These pictures are from her website. What’s great about this story is that a) she’s a woman, b) she didn’t have a math background beyond high school, and c) she was curious, worked at something, and found enjoyment and success.

I won’t go on and on here, but the other two stories with Marjorie’s in this issue of Math Munch are equally worth reading.

The pictures I’ve included here are some of Marjorie’s tesselations.

Ada Lovelace

It is always good to hear about female mathematicians. Today, Google featured a graphic with the tag “Ada Lovelace’s 197th birthday”. Investigation revealed that Ada Lovelace was the daughter of the poet, Lord Byron, and lived in the 1800s.

A paragraph in the Washington Post caught my attention.

At the age of 17, Lovelace was among the first to grasp the importance of Babbage’s machines, Google noted. In her correspondence, as reported by New Scientist magazine, Lovelace said that “the Analytical Engine weaves algebraical patterns just as the Jacquard-loom weaves flowers and leaves.” She also noted that the Analytical Engine “does not occupy common ground with mere calculating machines” and had the potential to run complicated programs of its own.

Apparently, Lovelace wrote the first algorithm designed to be run by the Analytical Engine. Some say she should be considered the first computer programmer.

Here is another Lovelace quote to ponder (from Wikipedia:Ada Lovelace)

[The Analytical Engine] might act upon other things besides number, were objects found whose mutual fundamental relations could be expressed by those of the abstract science of operations, and which should be also susceptible of adaptations to the action of the operating notation and mechanism of the engine...

Supposing, for instance, that the fundamental relations of pitched sounds in the science of harmony and of musical composition were susceptible of such expression and adaptations, the engine might compose elaborate and scientific pieces of music of any degree of complexity or extent.[58]

Visit from a future pilot

Kim Kast, amazing afterschool math teacher at John J. Flynn Elementary, contributed this piece. Thank you, Kim!
 
Last week, third grade math mania students enjoyed a visit from a special guest, University of Vermont student Sylvia Stevens-Goodnight. Sylvia just completed her sophomore year of study in the UVM College of Engineering and Mathematical Sciences. Her concentration is mechanical engineering, and she told the students she is one of only seven women in her program; she encouraged the students in their studies of math, and wanted to especially encourage girls to consider pursuing a career involving the study of math and science. Sylvia described some career-related experiences, such as trying on a pilot's suit, sitting at the controls of a jet plane, and even being ejected from the seat of the plane. Sylvia explained to the students that engineers sometimes design new products, invent new machines, and innovate new ideas. The students were surprised to learn that engineers could even design video games.

All of the students had many questions about engineering, and of course, about college life in general. The third graders couldn't believe that a student could have seconds, or even thirds, on ice cream for dessert... every night! Sylvia assured them (speaking from experience) that after a few days of all-you-can-eat ice cream, they would know why their mothers wisely told them, "Eat your vegetables!"