Showing posts with label teaching. Show all posts
Showing posts with label teaching. Show all posts

Sunday, October 9, 2016

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.

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.

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.


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.

Sunday, December 13, 2015

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.

Tuesday, December 8, 2015

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?

Sunday, February 8, 2015

From Lani Guinier


I am reading the New York Times on a Sunday, sitting next to the woodstove to keep warm. In an interview entitled Redefining Diversity, Re-evaluating Merit, by Tamar Lewin, Lani Guinier has some important things to say.

The score on your SATs or other exams is a better predictor of your parents’ income and the car they drive than of your performance in college. The credentials of our testocracy legitimize a new elite, and give them an inflated sense of their worth.

Diversity is not simply a matter of having people who look different sitting next to each other but learning in the same way.

Studies show that groups made up of the highest-performing individuals are not as good at solving complex multidimensional problems - like designing environmental policies, cracking codes or creating social welfare systems - as groups with a mix of skills, backgrounds and ways of thinking, even if the individuals in the group are not all high performers.

Guinier’s new book is called The Tyrrany of Meritocracy: Democratizing Higher Education in America.

Saturday, October 4, 2014

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.

Friday, August 1, 2014

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?

Saturday, July 12, 2014

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!

Monday, May 19, 2014

Who Gets to Graduate?


On Sundays I love to play tennis and read the New York Times. There was a great article this past Sunday. Author Paul Tough shares some sobering statistics about who is graduating with four year degrees, who isn’t, and why.

You must read the whole article. Go and do that now. My big takeaways: remedial classes and groups don’t work and students in some demographic groups (low-income, non-white, parents who didn’t graduate from college) are at risk but can be helped. It isn’t really new information. It is just more evidence supporting certain ideas.  I want to know how we can apply this to K-12 public schools.

Every college freshman — rich or poor, white or minority, first-generation or legacy — experiences academic setbacks and awkward moments when they feel they don’t belong. But white students and wealthy students and students with college-graduate parents tend not to take those moments too seriously or too personally...It is only students facing the particular fears and anxieties and experiences of exclusion that come with being a minority — whether by race or by class — who are susceptible to this problem. Those students often misinterpret temporary setbacks as a permanent indication that they can’t succeed or don’t belong…

“What I like about these interventions is that the kids themselves make all the tough choices,” ... “They deserve all the credit. We as interveners don’t. And that’s the best way to intervene. Ultimately a person has within themselves some kind of capital, some kind of asset, like knowledge or confidence. And if we can help bring that out, they then carry that asset with them to the next difficulty in life.”


Tuesday, April 8, 2014

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)

Tuesday, February 18, 2014

The Importance of Curiosity

One student was curious about tornadoes. Photo from NPR.

I look forward to getting the Marshall Memo via email. This week I found myself reading an Edutopia article entitled “Curious Homework: An Inquiry Project for Students and Parents” by Suzie Boss. It emphasizes the importance of curiosity in life and education, and laments the fact that students don’t always find a way to express their callings and passions in the context of school.

In the article, we learn about a teacher named Scot Hoffman who started his work on curiosity by bringing in folks with interesting careers or passions - a mountaineer, a doctor - and interviewing them in front of the students. Then it was the students’ turn to explore their own sense of curiosity. It would be fun to try this in the Burlington community, let students choose and interview folks, and partner with community members in addition to parents in order to pursue their own interests.

Saturday, October 26, 2013

Breathe collaboration

From Dan Meyer's You Pour I Choose Math Task

Steve Leinwand came to Killington, Vermont, on Wednesday night and I made sure I was there to see him. Dinner and the presentation by Steve was hosted by the fledgling local chapter of National Council of Supervisors of Mathematics (NCSM) called Vermont Math Leadership Council (VMLC). I made them a website at www.vermontmathleadership.org, where you can find resources shared by Steve, including his powerpoint from the dinner.

Here are a few things from the notes I typed on my iPad instead of eating dinner:

Take risks, make mistakes. The stuff we have now is bad. Enter the Common Core. Hope and change have arrived, like the calvary. This is a once in a lifetime opportunity to rescue ourselves and our teachers from all the problems we have had.

Effective teachers create language rich classrooms.

Effective teachers take every opportunity to build number sense.

Effective teachers embed math content and connect to the real world.

Effective teachers devote the last 5 minutes to formative assessment.

See Steve’s document called High Leverage Mathematics Instruction Practices for more.

I am not an effective leader if I don't breathe collaboration.

Monday, August 26, 2013

Stanford University: How to Learn Math

Image from Geometry Daily.


I can’t say enough about how fantastic Jo Boaler’s online math class was. I finished it yesterday.

Jo is a Stanford University professor, and she created a free, online class for teachers and parents called How to Learn Math. Students (there were approximately 35,000 people registered) watched videos, wrote responses to prompts, and completed other tasks at their own pace. Some are still finishing; the course ends September 28.

Jo is working on a course for young people now. She has published a book called What’s Math Got To Do With It. I’m convinced that whatever Jo does in the future, it will be great. Keep an eye on her.

In a nutshell, Jo is all about dispelling myths about who is good at math and who isn’t, evangelizing about the growth mindset work of Carol Dweck, and giving teachers ideas about effective math education. She advocates for math as an inquiry activity, and really seeing it in a totally different way than most of us were taught in school and continue to teach today.

In Jo’s words:

Mathematics classrooms should be places where students believe:

  • Everyone can do well in math.
  • Mathematics problems can be solved with many different insights and methods.
  • Mistakes are valuable, they encourage brain growth and learning.
  • Mathematics will help them in their lives, not because they will see the same types of problems in the real world but because they are learning to think quantitatively and abstractly and developing an inquiry relationship with math.

Sunday, July 7, 2013

Shrub

Edible Wasatch 2013, photo by David Vogel
My brother, David Vogel, and his partner, Rachel Hodson, are the owners and editors of a magazine called Edible Wasatch. It’s about local food in Utah, but I can’t wait for it to arrive in my mailbox in Vermont each season. It’s always full of gorgeous photos, great articles, and interesting recipes.

Shrub is the name of a syrup made from fruit, sugar and vinegar. I found it in the summer 2013 issue of Edible Wasatch I just received. You can add a small amount of shrub to seltzer water to make tasty, homemade soda kids will love.

Teachers and parents: Try making shrub with your kids. With this activity, you can combine wellness, local food appreciation, culinary skills, and math. What could be better? Then reward yourself by using some of the kids’ leftover shrub to mix up a delicious summer cocktail.

Strawberries have been so perfect around here lately, I think I would make shrub with those. However, you can use any fresh, ripe berries or other fruits. I have raspberries growing at my house now, so I might combine those with some local strawberries.

Here’s the recipe, straight from Edible Wasatch:
Basic Shrub
One part fruit or berries
One part sugar
One part vinegar

Wash and cut up the fruit and put into a bowl or a jar large enough to contain all of your ingredients. Add the sugar and stir or mash it with the fruit until it’s evenly distributed. Cover with cheese cloth or a kitchen towel to protect it from fruit flies and leave it to macerate - at room temperature for a few hours or overnight - until the fruit has broken down and become juicy.

Add the vinegar to the fruit and sugar mixture - apple cider vinegar or any kind of wine vinegar, not distilled vinegar. Stir or shake until the sugar is completely dissolved. Strain off the liquid and discard the solids. Store your shrub in a bottle in the refrigerator and enjoy for up to a year.

See their original article and recipe here.

Ideas for teachers and parents
Let kids do all the work, including deciding which fruits or berries are in season and would work well, picking or buying those, making the shrub, and making the soda. They could even sell it in the neighborhood instead of lemonade and hand out the recipe to customers.

Here’s some math. Ask kids things like...
  • What does “part” mean in this recipe?
  • How do we know how much of an ingredient to use when “one part” is called for?
  • How is this measurement different than other kinds of measurements we’ve seen in recipes (teaspoons, cups, etc.)?
  • How should we decide how much shrub to make?
  • How much fruit, sugar, and vinegar would we need if we wanted to double the amount next time we make it?
  • What would we do if we wanted to try making shrub that was less sweet?
  • Have you ever seen another recipe that called for “parts”? How could you figure out how much you need for “parts” when you know the total amount of the recipe you desire?

Other possible questions
  • If we use a few teaspoons of shrub to make homemade soda, about how much sugar will one glass of soda contain?
  • How does our homemade soda compare to a commercial soda? Amount of sugar? Type of sugar? Other ingredients? Taste? Color? Cost? Environmental and economic impact?
  • What does “macerate” mean?
  • What other ways could we use shrub besides making soda?
  • Why can shrub stay in the fridge for so long without spoiling?
  • What questions do you have?