STEM Show: a great end to a great week in Bermuda

(If you’re looking for the Belco STEM camp lesson web site, click here)

I think the Ascendant Group / Belco STEM camp for kids was a smashing success and started some conversations that we’re very motivated to continue.  Today was the final day of STEM camp for the week 1 campers.  Anastasia, Jocene, and Diane put together a little showcase and invited parents, Belco executives, the Ministry of Education, and the community to come and talk to the kids about their learning.  We were very pleased with the turnout and the enthusiasm at the STEM show.

First, Anastasia grouped the kids and assigned the groups to a station.  One group got to demo the Green City challenge, two other groups demonstrated robots, one group had an Energy station, and another group had a Web Design station.  Parents and supporters circulated around the stations for 45 minutes or so and asked the kids questions, which they answered excitedly.  The kids could talk forever about their week at STEM camp.

What I found fascinating is how in tune the Bermudian kids are with their own geography. They had some misconceptions about the advantages and disadvantages of certain forms of power generation – but they understood well the limitations of where they live.  Bermuda is on a seamount such that the land is slightly above sea level, a reef area surrounds the islands, and then it drops steeply into the ocean for thousands of feet. There are two other seamounts a few dozen miles away but then nothing else for hundreds of miles, until you get to North Carolina.  They could converse easily about the challenges of living here – having to import almost everything they need, including all fossil fuels – the importance of the tourism industry – the fragility of their reef ecosystem – the calm weather with occasional storms – the historical disappearance of native flora and fauna – the smallness and isolation of it all.  I wondered if kids in Colorado could tell you as much detail about our own geography, and I doubted it.

Logan, Cody, Cameron, and Darius teach their parents about robot design and programming

Derek and Andrew cover principles and tools of web design

Abbie, Brian, and Gabriel completed 5 challenges in the Green City!

Nasir kept his parents captivated for quite a long time, going over everything we did at STEM camp.

Next, we had a little graduation ceremony.  Anastasia and I each gave a speech about the creative problem-solving the students did over the week.  I talked about how real-world problem solving skills can’t be found in a textbook, and that students did important work when it came to teamwork, communication, analyzing tradeoffs, and doing research.  I complimented the students on a wonderful week.  We asked “wouldn’t it be great if school were like this all the time? This is what a STEM education is about. It is learning real-world problem solving by doing real-world problem solving.”  I also brought up FIRST Lego League, and I offered to collect contact information and help interested parents start a team or two.  I got some e-mail addresses and will follow up when I am home.

Anastasia showed a video about problem-based learning and explained her philosophy of teaching in an inquiry-based manner.  She summarized some research about creativity and its importance to learning, and how important creativity is for adolescent development especially.

Campers and their parents watch a video presentation.

We handed out awards – certificates of completion, and some awards of excellence for particular achievements in robotics, energy, and web design.  One of the Belco engineers, Don, had some “trophies” printed up on a 3D printer, and they were a big hit.

Team awards

Trophies from the 3D printer, some with moving parts

We mingled, cleaned up a bit, and then ended the camp.  I had a good conversation with Dr. Radell Tankard from the Bermuda Ministry of Education. STEM education is of high interest to the Ministry.  He asked in particular how becoming a STEM school had affected student behavior concerns. I told him that our data showed office referrals and discipline problems in general were way down, and we had data showing this was so. I cautioned that we had put a lot of other systems in place over the last few years, and that our discipline data couldn’t be isolated to STEM education.  However, I told him that anecdotally, the kids had fewer behavior problems when they were engaged and invested in learning during class time, and adopting the STEM philosophy really had improved student engagement.  We exchanged contact information – he wants more information!

Diane McCallum, who handled the STEM camp’s logistics beautifully, Dr. Tankard, from the Ministry of Education, and the very talented Anastasia Smith, camp director.

I loved working with Anastasia. She truly enjoys working with adolescents, and she’s very comfortable and at-home in the world of problem-based and project-based learning.  She came up with terrific lessons and learning experiences that fit the educational goals nicely. She trusted the students to be thinkers, and they were.  She works in North Carolina as a high school science teacher but is spending the summer in Bermuda.  It’s a shame she is normally so far away. I would enjoy working with her and hanging out with her.

A joy to work with Anastasia this week!

I feel really privileged to have been here for this experience. I’m excited to see where it leads and the conversations that are going to continue.  I know we’ll keep in touch with the community at Belco and the Bermudian Ministry of Education, and learn from each other the best way to engage students and invest in their future.

 

Day 4 Report: STEM in Bermuda

The STEM camp is so exciting and is going really well.  Jocene Wade-Harmon, the VP of Human Resources at Belco, deserves credit for her vision and persistence in pulling this project together.  Anastasia Smith is the director of the camp and she was such a perfect choice. Her philosophy toward teaching is that of giving kids space to be inquisitive and creative – creating experiences that will cause them to discuss, ask questions, and invent. She has done just that with some great lessons, field trips, and challenges during this STEM camp focused on energy.  Diane McCallum has managed the paperwork, logistics, money, transportation, and food just beautifully.

The kids have accomplished a great deal this week. They have built robots using NXT Mindstorms and gone through a series of tutorials learning how to program them.  Some kids really went above and beyond, and challenged themselves to do some great stuff just by asking themselves if they could. Can I make the robot navigate around obstacles? Can I make it chomp like a Pac-Man?  Can I give my wheels more power or more speed?  What happens if I change the radius of the tires or move the light sensor to another location?  They followed these tangents happily and sometimes created fantastic results.

Building, testing, and refining robots

The kids were introduced to the Green City challenge, in which the robots have to complete missions related to energy to gather energy bricks.  The challenges include spinning a wind turbine, fixing a dam, sorting the trash, replacing an old smokestack, and more.  Some kids have a couple of challenges complete and they are so excited.  They are learning about programming, algorithmic thinking, making trade-offs as far as speed/accuracy/point values, teamwork and organization.

Some of the students had programmed robots before, but there was a wide range of background knowledge and experience.  Several kids did not even have e-mail addresses.  They enjoyed learning the new technology, and they grew in their ability to program very quickly.

Another thread in the camp has been energy.  Bermuda’s energy is produced by diesel engines mostly, with a little biomass from their trash incinerator and a small amount of solar on private homes.  All of the diesel fuel is imported and is very expensive.  The island is very aware of the energy challenges due to their location and geography… but it also gives them opportunities.  The kids have discussed, sorted, and analyzed various sources and forms of energy.  They took home a spreadsheet to analyze their energy use at home.  Anastasia, Jocene, and Diane planned field trip experiences for them.  The kids are very articulate about their geography and the challenges it poses.  Bermuda sits on an extinct volcano, far from the mid-Atlantic ridge where it formed. The seamount is small, and beyond it, the ocean floor drops off precipitously.  The kids realize this makes offshore sources of power very challenging… yet the small area of Bermuda makes onshore power sources difficult too, and some are impossible (such as geothermal and hydroelectric).

 

A third thread in the camp was on sharing and communicating what they learned, and so we worked on some web design using HTML at first, and then Google Sites.  The students are working on a web site that explains to their parents, to Belco, and to the community what Bermuda’s energy future looks like.

Tomorrow is the students’ STEM show, in which they’ll share what they learned by presenting to the attendees of the show, and then we’ll have some presentations and awards by the teachers and staff. The Minister of Education will be in attendance, along with the executive team at Belco and perhaps the Minister of the Environment.

It’s been a wonderful week, and I definitely hope the momentum continues.  Belco is considering hosting a STEM club for students ongoing if volunteers can be found to run it.  Anastasia and I will appeal to parents tomorrow to consider creating FIRST Lego League teams for their kids, with mentoring and support from us in Colorado and space and equipment offered by Belco.  I think we’ll get some parents that want to take us up on it, and it would be a great start.

Ultimately, there are two separate missions I’d like to see Bermuda tackle.  One is the continual development of their gifted and talented students, to push them to go into STEM careers and stay in Bermuda to help with the little territory’s challenges.  The other is an equity issue.  The divide between the public and private schools, between the wealthy and the not-so-wealthy, is an unhealthy divide.  The kids in public schools with fewer resources deserve a great education that helps them develop their creativity and problem-solving too.  Both are workable with focus and vision from those involved – and it’s OK if it begins here!

 

 

STEM in Bermuda, Day 1

My family and I landed in Bermuda on Saturday night. We had a fascinating exchange with the women sitting in seats A and B in our row.  They seemed to be mother and daughter, and they were from Colombia.  They spoke not a word of English, not one bit.  And yet they were completely fearless in striking up conversations with me and my husband.  They asked for help filling out their customs and immigration forms, and we did the best we could, reaching far back into our memories for the Spanish words for “Date” and “Address” and “Business”.  And then we had to ask them whether they were carrying items for sale (“objetos… por (para?) vender?”), or “vegetales”, or “mucho dinero”?  I forgot the Spanish word for weapons, so we skipped that question and just told them to write “no”.

The two ladies kept asking us question after question, and I did the very best I could to answer even though I was only catching a word or two of every sentence.  They asked where we were from, and then where Denver was located, and they said they were going to Bermuda for something related to NuSkin.  They asked about the advertisements in the in-flight magazine.  They admired my daughter’s very blonde hair “Ella es gringa!” and asked to take a picture with our family.  It didn’t matter how uncomfortable I was with my Spanish, they talked and talked.  I walked off the airplane exhausted from trying to keep up with it, and a little in admiration of our Colombian friends who were so persistent in trying to get to know us.

My family spent Saturday night and Sunday sightseeing and going to the beach, and then on Monday the first Ascendant Group / Belco STEM Camp began.

I arrived at 7:30 and met up with Anastasia Smith, the camp director hired by Belco.  She had everything quite well organized and the camp was equipped with everything the students needed!  Each student had a labeled laptop and there were 10 NXT Mindstorms robots, enough for every pair of students to work with one.  She also had binders and gift bags for each student.  The schedule was a very busy one.  Monday we did:

a safety demonstration from the Belco safety department,

a paper tower “icebreaker” activity,

Paper Towers

REM Bot Building using the NXT Mindstorms kits (this is the standard educational robot that comes with the kit),

Lunch,

Lunch in the canteen

A tour of the Belco power plant,

Belco power plant tour. Bermuda gets most of its electricity from diesel generators.

and then about 45 minutes of web design.

Web design using HTML and Google Sites

 

We have hopes that the kids will work through many challenges in the Lego Mindstorms Green City challenge, discuss and understand Bermuda’s energy challenges, and create a web site describing what they learned during the week and proposed solutions to the energy challenges of Bermuda.  However, the goals are pretty lofty considering the timetable, so we need to keep in mind that the true goals are to:

* Allow kids to see STEM as an approach for solving the world’s problems

* Have the kids see themselves as engineers

* Steer the students on a path toward STEM hobbies and careers.

Bermuda’s educational system is at an interesting crossroads.  Of the students in the STEM camp, more than half are going to private schools.  Anastasia says there are more kids on the island that go to private school than public school now.  In a thriving educational ecosystem, private schools can prod the public schools to improve and bring the whole system up.  However, if the public school system is not healthy, the private schools further drain the public schools and the system becomes divided by class.  The island is very much aware of the need to revive its public schools.  The STEM camp is a first pass by Belco to bring some new energy into problem-based learning.

 

Sharing Ideas – in Bermuda!

Earlier in June, I had an interesting conversation with my assistant principal:

Me: Hi John, can I ask you a question about the computer lab?
John: I’m glad you’re here. I was just talking with our friends in Bermuda. They’re hosting a STEM camp this summer and they need a teacher with robotics experience to help them out with it.
Me: Wait. Help them out, as in?
John: In Bermuda.

I laughed, as I had just been talking with my husband and kids about reducing the complexity of our lives, slowing the pace and easing the pressure.  Saying no to more things, not over-committing.  But I told John I would think about it and discuss it with the family.  Although it doesn’t fit our new core values, we could not resist the opportunity.  I asked if I could bring the family.  We’re all going to Bermuda.  I will work, and the hubby and kids will sightsee during the day. We’ll have evenings and the weekend to have fun there as a family, and during the workday, I’m pretty excited about the opportunity for a little cultural exchange.

I am sensing an urgency from our contacts there to improve Bermudian education. The company that’s sponsoring the STEM camp is Belco – the Bermuda Electric Light Company.  What a terrific opportunity for the private sector to get involved.  They created an exciting summer enrichment for kids. It’s a deep honor that they selected Preston Middle School as a model for their camp, and we’ve been in touch with the territory’s Minister of Education to exchange ideas about STEM ongoing.

Preston is an exciting place to work. We believe kids should be engaged and inspired, that learning is an active, creative, rigorous, yet messy process.  STEM is one path to giving kids the tools to learn by solving problems.  The philosophy has really changed the culture at Preston. It’s energizing to be in a building where everyone buys into the idea that students learn by problem-solving together.  You walk down the halls and kids are huddled in groups, working on the challenges of transportation in sub-Saharan Africa, or building scale models of compost bins, or blogging about a peer pressure scenario.  

Belco has embraced this philosophy and has put together a great little program in which students will be tasked with solving Bermuda’s energy challenges.  The remote little island territory definitely has its work cut out for it, and the 12 – to – 15 – year – olds will be owning the challenge for the next generation.  The camp will involve Lego NXT Mindstorms challenges, energy activities, and web design. 

It’s going to be a great week and I can’t wait to see what I learn from it.  I also might get to check off a few items on my Bucket List – snorkeling at a coral reef has been on there forever!

 

 

Mother’s Day! Why my mom is awesome

My mom is a nerd and a genius.

She would always deny it.  Growing up, she told us often that she has dyslexia and found reading very challenging.  That she loved to learn, but couldn’t pull good grades in school, and it disappointed her family greatly.  I didn’t know back then if she even viewed herself as smart.  But she found ways to express herself through pure geekdom that more than made up for poor grades in school.

You won’t see many pictures of her techie side.  She’d always be the one behind the camera and behind the scenes.  She didn’t like having pictures taken of herself, which is ridiculous, since she’s beautiful.

My beautiful mommy and her brood on vacation in Montana

My mom was a stay-at-home mom and dad worked as an engineer.  My dad has his own awesomeness and his own geeky ways, but mom’s main way of expressing herself was to collect, and learn about, technology.

Early in her life, this showed up in mom’s moviemaking.  She used her dad’s 8mm camera to make her own special effects in this movie with her childhood friends.

In my childhood, she used my brothers and me as guinea pigs.  She thought it would be fun to teach us how Hollywood movie makers make fight scenes look so real, so she pitted us against each other in this little action movie.

As a child of the 1980’s, I grew up during a technologically AWESOME time – the very beginning of the home-gaming and home-computing era.  My mom was the driving force behind our family’s computing.  She and dad got us our first Atari 2600 game system in 1980.  She convinced the other neighborhood parents to get their kids systems too, so we could all game together. My aunts and uncles all got 2600 game consoles too.  We swapped cartridges often.

We never even got out of our pajamas on Christmas day 1980.

Mom took me and my brothers to our very first gaming competition at the local K-Mart. We participated in a Space Invaders competition.  I think one of my brothers won a T-shirt.

I don’t know why Pac-Man was at a Space Invaders competition, come to think of it.

By the time I was in late elementary school, mom had caught Atari fever and Atari had come out with a home computer.  She convinced dad to get the Atari 800xl computer.

The Atari 800XL Home computer (source: Wikipedia)

Our first home computer came with a TAPE RECORDER as a media storage device, and a BASIC cartridge.  I remember the anticipation of that first day as my mother popped in in the cassette tape for Crush, Crumble, and Chomp!  And we sat there for a half hour waiting for the game to load.  Then we played, but I think my baby brother hit the reset button and then we had to load it from the tape again.

Mom convinced a bunch of the neighborhood moms, as well as many of her own brothers and sisters, to get Atari computers as well, so we could trade cartridges and play games together.

Mom got a subscription to an Atari magazine (Antic!) and got a modem (I think it was 1200 baud).  We would dial numbers on our pushbutton phone and wait for a tone, then hopefully hang up the phone. We’d watch the lights blink and pray the connection didn’t get interrupted, which it did often.  Mom would connect to a server for an Atari enthusiasts’ club and download BASIC programs.  She and I would edit the programs, or sometimes we’d type in the programs from the Antic magazine and hope that they saved properly (which they often didn’t).  We eventually got a 5 1/4 inch floppy drive which helped the reliability a lot.  She introduced me to text-adventure games such as Zork and Planetfall.  I loved them and played all the time.

My seventh-grade gifted/talented project was to create a board game.  I asked my teacher if I could create a computer game.  I went home and, with mom’s help and troubleshooting, I wrote a trivia game in BASIC.  I brought it to school for my project demo, and it worked, but people got frustrated because the answers were case-sensitive and spelling counted.

I got a B.

When I was in junior high, I tried growing plants for my very first science fair project.  None of the plants sprouted.  I went to my mom three days before science fair and broke down in tears because I didn’t have a project.  She said she had an Antic magazine with a project in which you could turn Atari paddles into a lie detector.  She asked if I’d like her to help me make an Atari lie detector for my science project, and I said YES! So she did.

Science fair, junior high. Me with my Atari skin conductivity monitor (aka, lie detector). The 5 1/4 inch floppy drive was crucial.

I got a B.

My mom had a kindred spirit in our neighbor kid, Rick.  Rick’s mom was one of the ones she convinced to get an Atari 800xl computer so the kids could have fun with it.  Rick got his own subscription to Antic, and my mom helped him troubleshoot his own computer projects after school.  For science fair, Rick got his Atari computer to communicate with weather satellites and download weather maps. Mom spent a lot of time helping Rick with the project.

Rick’s science fair project and Antic magazine.

Rick got a B.  I think this upset my mom more than my B.  To be fair, neither of us used the scientific method really well, but Rick deserved an A.  It was a heck of an engineering project.  He printed out weather maps on that dot-matrix printer behind him.  None of the science fair judges really understood it, and I don’t think anyone really did except my mom.

The kid who won science fair that year did her project on paper towels. Whatever. Her mom doesn’t know her daisy wheel from her dot matrix, her RAM from her ROM, her kilobytes from megabytes.

In the 1990’s, we entered into Windows computing and the exciting connectivity of AOL and CompuServe.  I went off to college.  As her babies grew up, mom decided to get a part-time job.  She became a sales lady for Victoria’s Secret, working in their catalog office where you phoned in your orders.  She taught herself HTML and image editing.  She was convinced Victoria’s Secret was missing a big opportunity to enter online sales.  She reached out to the executive team a couple of times and even prototyped a web page for them, with an adorable animated gif of an online sales rep ready to take your order.  She was upset they never seemed to take her seriously, but she was right all along.  She left Victoria’s Secret after a while.  Imagine – hawking lingerie wasn’t really her thing.

Today, my mom stays active in tech by doing movie editing, archiving photos and family history, and troubleshooting her friends’ and family members’ computers.  She’s kind of an expert on viruses and malware.  We call her all the time when the computer is misbehaving.

Consider all this, and the fact that my mom has never had a paying job working in high-tech and has no college degree.  She taught herself everything she knows.  She’s the ultimate computer hobbyist.  That’s my mom!

Here’s mom today.  Beautiful and funny and savvy as always.  I love you!

Silly grandma has fun with the webcam.

End note: fewer than 10% of all Computer Engineering degrees are conferred to women.  I took my first programming course in college, and finally received my first A on a technology project.  I loved it.  I got a degree in computer engineering.  I wonder.. if there were more geeky moms to play around with computer “stuff” with their daughters, perhaps there’d be more of us.

 

Flipped lesson plan – intro to equations

This is about week 3 of flipping the classroom.  We are just starting our last unit of the year, which is on equations, equivalent expressions, and inequalities.  I decided to start this unit with a lesson on writing expressions and equations.  The students had previously learned the distributive property, so I thought I could extend that into distributive property with negatives, and combining like terms.

Common Core State Standards:

7.EE:

Use properties of operations to generate equivalent expressions.

1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

2. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”

In a flipped lesson, I have the students watch a video for homework that gives them background information or reviews old topics.  I made this video.  It’s not an amazing video, but I wanted them to review their understanding of profit, income, expenses, and how variables are used in equations.

http://www.youtube.com/watch?v=TDcII5U-7bw

In class, I checked to see if they had taken notes on the video.  About half the class did.  NOT GOOD!  This is a classic struggle of flipped teaching, isn’t it?  I had planned that if this happened, I would go ahead and do the opening problem anyway.  This one was designed to be *less* accessible without the video, but not completely inaccessible.

The students worked the problem while they also logged onto their Netbooks.  After a few minutes, I asked for answers.  They called out…. “350.”  “2100.”  “negative 50.”  “I also got negative 50.”  “1500.”  “Wait. I changed my answer.  Negative 50.”  “Negative 50.”  “Negative 50.”  I said we seemed to be reaching a consensus.  I asked for a few students to share how they got negative $50 for the profit.

One student said: “First, I had $1000, and then I multiplied $100 by 5 and got 500 and added that on.  Then, I took the $1200, and I multiplied $70 by 5 and added that to the $1200 and got $1550.  Then I subtracted $1500 minus $1550 and got the answer.”  I wrote: (1000 + 100×5) – (1200 + 70×5) and she said it captured her method.  I said she must have watched the video!  We discussed whether parentheses were necessary and the class decided they were.

I asked if anyone got the answer a different way.  Another student volunteered: “I got the $1500 to start, but then I just subtracted the $1200 and got $300 left to spend on T-shirts and legos.  But the T-shirts and legos for 5 students costs $350 and so that’s more than you have.”  I wrote: 1000 + 100(5) – 1200 – 70(5) and asked if that basically explained it.

A third student offered that we basically start $200 “in the hole” and so we would need to make up the $200 with the student fees.  But if you take the -200 and add 500 for the fees and then take away 350 for the other expenses, you still end up $50 behind where you started.  This expression was: -200 + 100(5) – 70(5).  I told them I thought it was a clever strategy to combine the fixed income and expenses into one number.

We took note of the different strategies and it was time for one more quick mini-lesson before diving into work time.  The students went into Google Docs and opened a spreadsheet.  I taught them directly how to create a table for the function y=30x+12.  We created a column of x values, increasing by 5 each time.  I showed them how to enter a formula for the y-values and drag down the table to complete it.  Most students had not done this for a long time and needed the review.

For fun and spiraling, 🙂 I asked volunteers for a real-world situation that might match the equation y = 30x + 12.  One student offered (I loved this answer):  “You have a countertop.”  I said, “Describe the countertop.”  He suggested, “It, like, has a part sticking off the side you could set your baby on, and it’s the 12.  Then the big part of the countertop is 30 wide and the height is x.”  He drew:

Another student offered: “You have 12 dollars now.  And you’re selling something, and the thing you’re selling is 30 dollars each.”  I said, “So what’s x?” And she said, “However many of the thing you sell.”

It was time for the cookie problem.  I love this problem because it doesn’t have an easy mental-math solution – the spreadsheet is a very handy tool for reasoning out how many cookies you need to sell.  I presented the problem of owning a business making cheap, processed cookies and told students they should write down important information.  Students asked if they could take pictures of the problem with their phones, and I said they could.

I showed the students just how to get started with “Cookies” and “Income” columns in their spreadsheet, and I gave them the instructions to use the spreadsheet to figure out how many cookies they should sell to break even.  As students worked on their spreadsheets, one young lady waved me over and asked “Don’t you basically make 7 cents per cookie, but since you have $2000 and you pay $6000, you just need to see how many times 7 cents goes into $4000?”  She was combining like terms in her head! I said that she should give it a try and see if her answer comes out reasonable.  I also asked if she thought she could calculate profit for any number of cookies using what she said.  She nodded and started in on her spreadsheet.

Many students had a spreadsheet that looked like this after a while, so we did a catch-and-release to see what everyone thought and where we were going next.

Their income was not getting close to the expenses very quickly.  The students could tell they were not making a profit yet, because the expenses were so high.  Some couldn’t tell if the cookies would ever make a profit.  Others had used the formula “0.5 * A2 + 6000” for expenses, making their expenses grow faster than their income, which was really confusing.  I asked the student who combined like terms to share how many cookies she thought we needed to sell.  She explained that 7 cents goes into $4000 over 50,000 times.  Students wondered if they had to add that many rows!  I suggested they just increment x by a different number.  Perhaps 1,000 or 2,000?  Who could figure out the exact number of cookies needed to break even?  Some kids did make a third column for “profit”, subtracting the expenses from the income. This was helpful to them as they looked for the break-even point.

I released them and they worked a bit longer.  Eventually almost everyone determined the number of cookies would be between 50,000 and 60,000, and some students even figured out the answer precisely, although by different means.  One student figured out if he made x increment by intervals of 584, he could get within $6.00 of the break-even point.  Another student played with two rows of the spreadsheet until the profit got as close to zero as she could get.  A few more students used calculators and divided $4,000 by 0.07 to find the exact number of cookies needed.

This student figured out if he incremented by 583.2 cookies, he could get very close to the break even point.

The lesson was overall a very good one and the students were really engaged.  I can tell when a lesson is a good one by the number of kids that approach me for bathroom breaks.  NONE!

I would like them to play with the ideas of combining like terms, distributing a negative, and solving equations more tomorrow – and then they can start learning how symbolic manipulation can help them solve equations more efficiently… and that is when it makes sense to use symbolic manipulation!  I’ll have to look around for videos! I know there are a lot available already.

 

Flipping the Classroom.. Just Getting Started

One of my professional goals for the year was to use technology more effectively, so I focused a lot of my efforts at first on using Google Docs and presentation software for kids to do cooperative learning.  I have been pleased with how that’s come along, and now I’ve decided to experiment with flipping the classroom to see how it goes.  I’m passing along advice I’ve picked up that seems to help.

1.  Set norms and expectations.
I let the kids know this unit would be done differently and said I was experimenting with doing practice in the classroom and lecture as homework.  I told them I needed buy-in from everyone and they had to agree to watch the videos if we could be successful with an agreement of not having homework.  If I assigned a video, they were to watch it and take notes as expected.

2.  Accountability should be built in.
One of my colleagues said it’s been helpful for her to structure an activity the next day that requires some knowledge of the material in the video to be successful.  Kids may be able to pay very careful attention to the opening problem and catch on, but the activity should be more difficult without the background knowledge from the video.  I did this for my flipped lessons and found it was a powerful motivator.

My colleague will sometimes give kids a pre-quiz at the beginning of class to see who watched the video.  Kids can sometimes pass the pre-quiz without watching, but in that case, it is clear they didn’t need the video to know the material.  I am not yet doing a pre-quiz, but I’m taking a cruise around the classroom with a clipboard to jot down who took the notes from the video, and giving participation credit for that.

3.  Keep it short, keep it simple.
I am choosing not to assign long videos.  If it can’t be explained in 15 minutes, I will create my own video that trims it down.

3. Use a variety of practice in the classroom.
I like doing cooperative learning and inquiry in the classroom, but if I’m not assigning simple practice as homework, we need to make time for this in class.  I decided to provide some richer tasks for group work and also a few practice sheets for solo time.

Here are the first 2 lessons I put together using the flipped model.  Overall, I was pleased with how it went and look forward to doing more of it!
Lesson 1:  Using flat patterns to understand surface area and volume of triangular prisms
Grid Paper for taking notes during video lesson:  flat pattern grids
Video 1: Sketching rectangular prisms and flat patterns (Nets)
Video 2: Khan Academy: Volume of Prisms
Opening Questions: sa_v_opening  Kids worked on this while I checked off their notes and conferred with them.  Then I called on “volunteers” to share answers and discussed how it related to the videos
Group Work time:  flat_pattern_groupwork  Students worked on this in groups of 3 or 4.  Their task was to create a rectangular box with certain constraints, and then imagine cutting it in half to make triangular prisms and design a flat pattern for the triangular prism.  The purpose was for students to move beyond the idea that volume was always length x width x height, and see it as the area of the base x the height.  We started with triangular prisms so we had models to work with.  I also wanted them to see that the surface area would not be cut in half and be able to describe how to find surface area of a triangular prism.
Practice for the next day:  fancy_sa_volume  After reviewing the learning from the day before, we discussed the idea that a prism always had a volume of (Area of the base) x (height).  I gave the students this sheet for practice.

Lesson 2: Describing how to find the surface area and volume of a cylinder
Video:  Khan Academy Cylinder Surface Area & Volume
Opening: cylinder_warmup Students worked on this while I checked their notes and conferred with individuals.  Then we discussed the opening problem and how the volume of the cylinder related to the cube with the same height.
Group Work Time:  Not finished yet!  We just did this lesson before the weekend.  We’ll have a problem solving activity involving cylinders that the students will be able to do in groups.
Solo Practice:  Khan Academy Practice on Solid Figures Kids can work on this as review / drill and gain points on Khan.

Reflection for me:  My favorite part of the classroom flipping is that when we have practice, I can watch each student work through the problems and make sure they understand the content before moving on.  With homework, I lose that information flow.  Since we worked on the practice for Lesson 1, I have marked up student work and will return it to them to fix and make right before they can do the Khan assignment.

I won’t commit to full-time flipping yet, but I like what I see so far and would like to try it for our algebra unit as well!

 

 

 

 

 

 

Why I Like Geology

If I could do it all over again, I’d be a geologist!

Earth science is fascinating to me. I like thinking about the Earth that used to be, the Earth that might be in the future.  I like looking closely at the rocks and imagining what kind of world created them, and thinking about how they’re currently dying and being destroyed to start the cycle over.  My daughter wanted to study plate tectonics for her science fair project, so I suggested we drive around and look for evidence of tectonic activity just outside town.  In northern Colorado, there are rich and interesting places to study geology and I thought it would be a shame for her to do an earth science project at a desk!  So we drove around and looked at rocks.

We found marine fossils embedded in the limestone near home.

Sea creatures

We dug into the shale at a roadcut.

Uplifted shale and Dakota Sandstone

We ran our fingers over the conglomerate at a rock climbing area.  I marveled at the Morrison Formation under our feet, which has yielded a very rich trove of dinosaur fossils over the years.  Who knows what could be right under us!

Conglomerate. Once, there was a mountain. Pieces of it washed away and got cemented into a new rock, then that rock got uplifted and became.. a new mountain

We felt the gritty sandstone at base of the red cliffs of the Fountain Formation, like bookends on either side of a mountain.

 

We visited Horsetooth Mountain Park and examined the ancient schist and pegmatite.

It’s all metamorphic and schist.

Pegmatite granite. Igneous rock

 

We downloaded a free geologic map from the USGS for the project.  What a wonderful resource!  My kid organized her rock information and made a presentation board, and of course I keep thinking and thinking and thinking about rocks.  It made me understand the reasons I like geology as much as I do.  As a “math person”, it appeals to me because it has logic-puzzle features.  I like looking at the evidence around me and reasoning out the history of the area.  As with all logic puzzles, there are a few simple rules and likely only one correct solution.

– Sedimentary rocks are created in more-or-less flat layers.  Newer layers are always created over the top of older layers.
– Igneous rocks can intrude into other rocks.  If an igneous formation cuts through another rock formation, it’s newer than the surrounding rock.
– Faults can cut through other rocks.  A fault is newer than the rock it cuts through. Rock that overlays and covers a fault is newer than the fault itself.  Uplift happens after the sedimentary rock has been deposited.

I know less about the formation of metamorphic rocks and so my rules for them are incomplete.  But using what I know, I can look at the map and at rocks around me and build a geologic history of the area.  The rocks had to have been created in a certain order, and so a story starts to weave itself.  First there was rock, and then metamorphism, and then igneous intrusions, and then came the sandstone, then some faulting, then the shale and the dinosaurs, then more sandstone and then more dinosaurs, and then there must have been a time of erosion, and then more faulting and so on and so on.  I like to look at the map to see if I came to the same conclusion as the geologists who made it.

As much as I want to help my kid learn about the scientific method, all I keep thinking about is what a cool puzzle it is to piece together the history of northern Colorado!  Is that science, or more mathematics?

 

 

Cooperative Learning – a good lesson for me

I got a reminder this week on the importance of cooperative learning!  I’m a little embarrassed that I needed the reminder, but I think during busy times, we tend to forget about what’s important.

The students have been learning about circles. (Anticipating Pi Day!! Yahoo!)  We’ve watched video tutorials on circles, done whole-class instruction, worked drills online and on paper.  I wanted them to start synthesizing what they’ve learned by combining it with their problem-solving skills and their previous knowledge of area and perimeter.  So, one day, instead of our usual warm-up problems, I distributed this problem set and told the kids to work them solo.

 

I gave the students a few minutes of struggle time and then told them to share out their answers.

The results were so disheartening!  Students didn’t know whether to calculate area or circumference – or do neither.  Very few students made any progress with the pizza problem.  The most common mistake by far was to just divide the price by the diameter.  We JUST finished studying unit prices, too! They had learned about area in the past, and about perimeter, and I could not understand why this was giving them so much trouble.  The cognitive effort was low and engagement was low as well – so I could also not understand if it was a difficult task or if the problem was more one of effort and engagement.  I made a note to come back to these topics.

I did not do any additional teaching between that set of problems and today.  We reviewed formulas, but did not tackle the idea of problem solving in whole-class instruction.  Today, I decided the kids have the skills necessary to solve the problems. They just needed to explore the ideas and discuss them with a group to sort out their misunderstandings.  I created a new problem set:

 

I realize the picture is hard to see, but they’re basically circle problem-solving questions along the same vein as the pizza and basketball problems.  I don’t tell them whether to use circumference or area or both or neither – the students need to analyze the problems and develop a strategy.  Exactly the same skill set.  However, I set it up differently this time.  I did not give the kids a few minutes of solo work time followed by going over answers.  I said:

As a group, you will need to analyze these problems and figure out how to solve them.  By now, you know my expectations for group work.
– Select a leader.  This person will read the questions and make sure everyone is doing the same problem together.
– Give everyone a chance to contribute, and everyone must also have a chance to listen.
– Thinking out loud while you’re working will help you solve the problems successfully.
– Stay on the same problem at the same time.

The difference was truly amazing, and it reinforced that my students DID have the necessary skills to solve these problems, and they COULD synthesize ideas – but they had to discuss their ideas and explore them together.  Our group work isn’t perfect, and I know many teachers do a much nicer job at coordinating cooperative learning than I do.  But I looked around my noisy, busy classroom and there was great math going on.  They were engaged in the task and vigorously debating the solutions.  They were excited to share their answers and give feedback to their peers.

Group work didn’t always look like this.  Early in the year, the focus was much more on how to behave properly in a group setting and not as much on the math.  It took lots of practice for the students to settle into it!  But now, we’re a little more of a community and the kids have expectations of each other.  They know what good group work looks and feels like.  They have come a long way.
I needed that reminder – that even during busy times, when you don’t think you have the time or energy for the messiness of cooperative learning, it’s a key ingredient for anyone to really do any complex thinking.  I feel my students gave me a great gift by reminding me of what they are capable of!

 

 

 

Probability Pi Day Carnival, Part II!

Here’s how the Pi Day preparations are going and what the students are up to.  There is some great math going on, and every year I enjoy this project more and more.  I always finish the unit wondering why I don’t do more project-based learning.

First:  Students need to create a game, and write the rules for it.  They have to determine how much you pay to play, and include how much you win for various levels of prizes.  The math has to contain multiple probabilities or multiple events to get an advanced grade.  This group of students has a game where you pick a card, which has a fraction on it from 1/5 to 4/5.  You turn around, and they put pigs under the buckets such that the fraction represents your probability of revealing a pig.  When you choose a bucket, you win a prize if you find a pig.

Sort of a Monty Hall idea?

Second: Students need to calculate the theoretical probability of winning.  They need to show how they arrived at the probability.

This group used a counting tree to determine the probability of drawing two matching puzzle pieces.

This student uses Area = pi x r^2 to figure out the probability of throwing a ball through a precisely measured circular hole.

Third: Students have to test their game 100 times to determine the experimental probability, and discuss differences between experimental and theoretical probability.  Games of skill often have a big difference between experimental and theoretical, while pure chance games are very close!

A student intern tries to put these 5 jars of candy in the right order, blindfolded.

 

These students roll marbles onto their target area.

Fourth: Students have to make predictions based on their probabilities, to help the carnival organizers determine how many prizes they’ll need to buy – and to make sure their project will make a profit!

These students say the buckets will be full of prizes for their duck game. How full though?

 

Lastly, the students make a presentation pitching their game to the carnival committee, and the committee determines which games make the cut.  We pick about a third of the games to represent the school in the big Pi Day carnival after school.  The rest of the games will be played in the class mini-carnival on the day before Spring Break.

This young man couldn’t decide on a name for this spinner game, but thought “The Wheel of Awesomeness” would help in his sales pitch.

These students collaborate on their presentation using Google Docs. Their game is called “Flash Dice”.

 

On March 14, after school, we reserve the gym.  We set up a table for each group and allow them to come set up their project.  We sell tickets for ten cents each, and provide each group with some tickets and a small bag of candy to give away.  If tickets are given as prizes, they can be entered in a big raffle drawing.  We also have food, drinks, and a silent auction.  It ends up being one of the biggest events of the year, and it’s a celebration of math!

 

Photos of the big day coming soon.  I will also post a grading rubric for the projects!