6 mathematics problems based in everyday life on the Galápagos Islands

At Teachers2Teachers, it’s a given that we love numbers, but we suspect that we’re not alone. The human brains must inherently love numbers, otherwise why would numbered lists on the internet be so clickable? So we’ve succumbed to temptation and come up with a list of six real-world math problems set in the Galápagos Islands.

Teachers can use these problems and others like them to bring math alive in their classrooms. Putting numbers in a cultural context engages students and fosters a love of STEM. The knowledge gained also has value.

1. Counting the number of magnificent frigatebirds able to nest in a certain area.

This allows an assessment of the sustainability of hunting and feeding resources.

2. Predicting the growth of the islands’ human population.

By law, 97% of the islands is preserved as park, so the number of residents must be strictly managed.

view of galapagos promontory

3. Calculating the speed at which a blue-footed booby dives into the water to capture a fish.

This figure (an incredible 60 mph, ouch!) explains the uniqueness of its skull shape.

4. Estimating the number of blacktip sharks that visit the dock area in Puerto Ayora.

The health of the ocean ecosystem can be assessed by how stable this number remains.

5. Measuring the acreage taken over by invasive plant species.

Conservation efforts to preserve the natural environment are informed by understanding the obstacles.

6. Estimating the age of a tortoise based on its size.

The presence of larger, older tortoises means a species is thriving.

 

With thanks to Jonathan Drake for most of these photographs!

Finding Mathematics in All the Right Places

In our previous post, we mentioned how fortunate we felt to have assembled a dream team of mathematics and science educators to travel to Guatemala with us. The dream continues with this installment. Board member Linda Gojak, whose extensive resume includes the presidency of the National Council of Teachers of Mathematics, shared her expertise in a visit to Costa Rica and Guatemala with T2T staff member Becky Adams. Here are some of Becky’s reflections….

Master mathematician Linda Gojak tackles the coffee-bean challenge

On our second day of visiting several wonderfully unique schools in San Ramón, Costa Rica, our foursome (including Dustin Dresser of Costa Rica Frika) sat down in a German bistro in the city center.  While waiting for our decadent, coffee-flavored milkshakes to arrive, we noticed that the table top was filled with loose coffee beans underneath a sheet of glass. Typical of T2T educators, our conversation about the beans quickly turned into a mathematics estimation problem!

Bean There, Done That

For the next half hour, we became proverbial bean-counters, extrapolating the numbers we generated and arguing about the depth of the inset portion of the table that housed the beans. Although we never came to a final conclusion about the total number, our devoted crew demonstrated that T2T’s goal of making cultural connections works in every country!

Coffee milkshake deliciousness in Costa Rica

Our conversations about mathematic education continued throughout our visit as we visited five very different schools, each with its own approach to learning. What all these schools had in common was intense pride in their students and communities. Our favorite highlights included an elementary school housed in a stunning historic building in downtown San Ramón and an agricultural high school that produced its own phenomenally delicious ice cream.

We were able to keep busy because of the hospitality of T2T friends Tina and Carlos Sandi, who provided a home away from home. Their warm family and peaceful setting, while commonplace in this country, was a welcome respite from our packed-full days.

Although we would have loved to stay longer in Costa Rica, Linda and I said adios to our newfound friends, giving our host mascot Ruffle the Chihuahua one last pat. Our next destination was waiting for us three countries north on the Pacific coast.

Dream Team Strikes Again

Anybody who has ever traveled with T2T-I to El Paredón, Guatemala, can attest to the instant love created by this community and our local partner organization, La Choza Chula. This trip was no different. Linda and returning presenter Tim Quiroz wasted no time in getting to work with the El Paredón teachers after T2T staff led a fun-filled, early morning team-building session.

oval plate with whole fish, beans, rice
No fish were harmed in the writing of this blog

By the end of the day, Linda and Tim had helped the local teachers discover new mathematics teaching strategies and inspiration. A guiding principle of every T2T seminar is that the presenters and local teachers arrive at education solutions together. So, even though Linda and Tim may have had more training in pedagogy, their goal is to empower the local teachers to engage their students.

Day two gave the teachers time to plan lessons implementing these ideas with Linda and Tim’s support. The seminar culminated with an enthusiastic discussion about how the teachers were building engaged, empowered learners in their classrooms.

Finally, with affectionate hugs and promises to return, the T2T team headed back to home base, but not without stopping first for a fabulous meal of fish and rice from a renowned nearby restaurant. Since our table didn’t display coffee beans, we counted our blessings instead.

In El Paredón, La Choza Chula teachers show their certificates, with Tim Quiroz (second from left), Linda Gojak (fourth from left), T2T staff members Lucía Dávila (middle, standing) and Becky Adams (far right)

 

The S in STEM

What are some famous pairings that you can think of? Peanut butter and jelly, Fred and Ginger, shoes and socks, Microsoft and Apple…the list goes on. What about science and mathematics? They are often spoken of as two complementary disciplines, but what education experts will tell you is that their overlap can disguise important distinctions.

T2T-I’s coaching visits to the William M. Botnan school in the highland town of Santa Avelina, Guatemala, typically focus on mathematics. So we were excited that our recent trip included Professor Dan Levin, who teaches students at the University of Maryland about science education strategies and practice. Written by Dr. Levin, here’s a behind-the-scenes look at how he highlighted the S in STEM.

 

Day 1

The overall goal of this seminar was to help teachers plan lessons to elicit their students’ mathematical and scientific reasoning. The metaphor of a coin was introduced to the teachers, where one side of the coin represents students’ thinking and talking, and the other side emphasizes the teacher listening to the students’ thinking and talking. Students reason, explore, and explain, while the teacher listens and guides them if needed. Both elements are necessary for effective instruction.

The exploration-before-explanation workshop had three main parts. The teachers would:

  1. Participate in a lesson where the local teachers experience the two sides of the coin, doing the thinking and talking while the T2T team listened and responded
  2. Discuss the thinking that the teachers expressed during the lesson
  3. Begin planning lessons to apply this thinking/listening strategy in the teachers’ classrooms

 

 

I began by posing a science question to spark discussion among the teachers as they took on the role of students. I like opening this way because it’s fun, and because it reminds us that science is about exploration, discovery, excitement, and understanding. It’s P.E. for the mind. Also, if we expect science teachers to push their students to reason, we must provide them opportunities to push themselves.

I had purchased some basic supplies during our overnight stop in Chichicastenango. I swung a bead on the end of a piece of string and asked, “If I were to swing this bead back-and-forth like this, and cut it when it reaches its highest point, just when it is about to come back down, what will happen to the bead?”

(To have some of your own fun, you might take a moment here to consider what your response might be!)

After briefly talking in pairs, the teachers’ ideas began flowing rapidly. One teacher suggested that the bead would fly back in the direction it came from on an angle. I asked the rest of the group what they thought about that idea, reminding them that science progresses through disagreement and debate. Arguing about scientific explanations creates greater understanding.

A second teacher asserted that since the bead has its own force and momentum, it would fly off in the direction it was heading. The computer teacher then pointed out that when the bead was ready to come back down, it did not have any force acting on it except gravity. Therefore, it would fall straight to the ground.

In debating these different solutions, the teachers readily drew on their experience of being on a swing. They questioned exactly when the string is cut and what ideal conditions are presumed. My next step was to give each pair of teachers a bead on a string to try out different ideas and revise their explanations. Finally, we came back together and discussed our thinking.

At the end of our investigation, someone asked me for the answer. First, I reminded teachers that the finding the “right answer” might not necessarily be our only goal in the classroom. Before explaining more about that, however, I explained what a “physicist would say” in the idealized problem: when the bead is just about to come back down, it has no velocity and no momentum, and the only force acting on it is gravity.

But how to define a right answer in a science lesson? Is it simply what would happen to the bead? Or is the right answer the students’ application of concepts of force, momentum, velocity, and gravity in their pursuit of an explanation?

And when is the right answer important? Do students have to know the right answer at the end of class? Or could they have time to reconsider it, review the arguments, try out new things, and question their own understanding? Instead of revealing the correct answer, if we had been continuing to work on this problem, I might have sent them home to think or write about it.

Finally, we introduced the tools that we thought the teachers might use in planning science lessons. For example, I described the 5E instructional model — engage, explore, explain, elaborate, and evaluate. The Spanish equivalent is emocionar, explorar, explicar, evaluar, and elaborar.

 

 

While not a magic lesson plan format, this sequence allows teachers to consider the opportunities for students to reason (the tail side of the coin) before they, or the teacher, explain it. We shouldn’t necessarily expect that students discover all knowledge on their own, when history tells us that scientific knowledge and theory have been developed and refined over centuries. After all, Aristotle knew less about the variety of chemical elements than does today’s eighth grade student in Santa Avelina. Nevertheless, students should be doing the reasoning, and teachers should help them use their reasoning to understand scientific knowledge and practice.

The rest of the day was spent introducing additional teaching tools and planning science lessons. Each teacher had an opportunity to describe her or his lesson plan. We gave feedback and asked them to give each other feedback, using a list of questions for guidance. I was excited to hear that all the teachers planned to use the lesson they had just constructed in their classrooms the following day.

Day 2

I visited the sixth grade class the next day to observe a lesson on the teaching of practices of experimental scientific investigation. In our workshop the day before, the teacher, with the help of a colleague, had designed a lesson to teach students particular elements of scientific practice, such as questioning, hypothesizing, and concluding, by first having them explore a phenomenon.

He began by explaining to the students that we all have questions, and that questions are important in science. He asked the students what kinds of questions they had. It was clear from his attentiveness that he valued his students’ ideas.

The results — an egg floats in salt water

He then told the class that he had a question he wanted them to explore — what would happen if he placed an egg in fresh water and what would happen if he put it in salt water? Students came up with several ideas. Some thought it would float in salt water or fresh water, while some thought the opposite. Some thought other things might happen, such as the egg exploding.

Again the teacher was receptive to all ideas. He had a greater point than whether the students were correct or not. He wanted them to understand that they had been making hypotheses.

The rest of the class continued in a similar way. Students observed the egg under both conditions and confirmed that the egg floated in salt water and sank in fresh water. The teacher identified this as their results. He then asked them to explain why the egg floats in salt water and sinks in fresh water. Collaboratively, the class came to agreement that the egg sinks in fresh water because it is more dense than fresh water, and the opposite is true in salt water. This explanation, he revealed, was their conclusion.


Dr. Levin continued to observe the other grade-level classrooms, meeting with each teacher individually to answer questions and offer impressions. T2T-I would like to thank Dr. Levin enthusiastically for giving his time to the teachers in Santa Avelina. With more effective science instruction, the 167 students at the William M. Botnan school will have opportunities open to them to that were closed off from past generations.

 

Further Reading

Bybee, R. W., Taylor, J. A., Gardner, A., Van Scotter, P., Powell, J. C., Westbrook, A., & Landes, N. (2006). The BSCS 5E instructional model: Origins and effectiveness. Colorado Springs, Co: BSCS5, 88-98.

Hammer, D., & van Zee, E. (2006). Seeing the science in children’s thinking: Case studies of student inquiry in physical science. Heinemann Educational Books.

Levin, D.M., Hammer, D., Elby, A., and Coffey, J. (2012).  Becoming a responsive science teacher:  Focusing on student thinking in secondary science. Arlington VA: NSTA Press.

National Research Council. (2013). Next Generation Science Standards: For States, By States. Washington, DC: The National Academies Press.

Robertson, A.D., Scherr, R.E., and Hammer, D. (Eds) (2016) Responsive Teaching in Science. London:  Rutledge.

Wiggins, G. P., & McTighe, J. (2005). Understanding by design. ASCD.

A New Way to Support Teachers

Written by Executive Director Chadd McGlone

T2T-I has a new word in its vocabulary of programs: seminar. In Spanish, it’s capacitaciones pedagógicas. Given that we’re providing seminars in STEM education, we’re considering coining the term STEMinars. You heard it here first, folks!

To explain why we needed another name in the first place, we need to go back in time to 2014. T2T-I grew out of a desire to connect teachers in the U.S. with teachers in developing countries to build long-term, deep, two-way partnerships. We initially thought that one-week trips to connect in person during summer breaks would meet everyone’s needs.

When we saw the excitement among the local teachers in Guatemala and Ecuador, however, we couldn’t be content with continuing the relationships long distance throughout the other ten months of the year. So we organized some smaller, shorter visits to provide workshops that filled in and built on the changes begun during Teacher Trips.

T2T-I Board Member Francisco Alarcón leads a workshop for teachers in Santa Avelina, Guatemala

These experimental, two- to three-day visits were so well-received that this week marks our third one. To make them official, we’ve dubbed them seminars and capacitaciones pedagógicas. Once again, we have some amazing educators joining us.

The STEM Dream Team

Our dream team roster begins with three board members: Arthur Powell, Steve Rasmussen, and Leslie Babinski. Arthur and Steve have both offered their significant expertise with T2T-I before, even traveling as far as the Galápagos Islands to coach local teachers. Leslie has managed to extract herself from her busy job on the faculty at Duke University to help T2T-I take an important step in measuring impact.

Tim Quiroz, a teacher trainer from Santa Barbara, California, is returning on his fourth trip with T2T-I in one year. Tim’s goal for this visit will be helping teachers connect literature, games, and mathematics. His workshops are always popular.

From the University of Maryland, Dan Lavin joins us for the first time. He is a science education professor and the fifth person from UMD to participate in a T2T-I program in the past nine months. Dan has planned some great science education lessons that will show teachers how to incorporate local wildlife and materials.

Our final two team members are also first-timers: Jere Confrey and Alan Maloney.  Jere is a mathematics education professor and Alan is a research scientist. They have together founded the Learning Sciences Group, which combines educational research with advanced technology to benefit middle grades mathematics students.

Where are They Going?

These seven experts in STEM education will offer seminars in four locations in Guatemala —

  • El Paredón – Arthur, Steve, Leslie, Dan, and Tim will join T2T-I staff BeckyAdams, Lucía Davila, and me in this lovely coastal surfing town. We will spend the first day in workshops with the 24 local teachers and then during the second day focus our time in their classrooms. This visit to El Paredón is T2T-I’s third, and we’re always moved by how warmly the local teachers welcome us. Some of them even traveled inland to Antigua to attend the conference we organized last November.
  • Antigua – Jere, Alan, Steve, and T2T-I Country Director Manuela Cea-Poblete will be in this historic colonial city meeting with some of our partners and working with the leaders of our Center for Education, which was recently renamed ANIMATE. (Animate in Spanish means to motivate or enliven, and it contains the word for mathematics, too, which is mate. Pretty cool, eh?) They will also participate in a team workshop.

    Lago Atitlán with volcanoes
  • Santa Avelina – Arthur, Dan, Becky, and Hans del Cid will travel to Santa Avelina to hold a two-day workshop with the 13 teachers at the William M. Botnan school. One of our favorite schools to visit, this gorgeous highland location not only has its very own waterfall but overflows with hospitality.
  • Panajachel – Our partner Starfish Impact invited Steve, Jere, Alan, Manuela, Lucía, and I to their brand new school serving upper-grade girls. We will meet the teachers, observe their classes, provide coaching, and plan future collaboration. Given that this town is on the northeastern shore of Lake Atitlán, surrounded by three volcanoes, we’ll soak up the stunning views while we’re there.

Bearing Gifts

A final note of gratitude is due to ETA/Hand2Mind for the manipulatives and Cuisenaire rods they have donated to each of these schools. Not to be confused with Cuisinart kitchen tools, Cuisenaire rods are colored, segmented sticks that allow elementary students to build their understanding of fractions. We love distributing these resources because they enable student-centered learning while at the same time creating enjoyment.

All of this takes place in the span of ten days, and I could not be more grateful to the T2T-I staff in Guatemala for their precise coordination of its many moving parts. To get seven visiting experts to four communities to serve 37 teachers with a reach of over 1000 students, the logistics require a top-notch team. Thank goodness that’s exactly what we’ve got!

Practicing What We Preach

An interesting concept in mathematics is exponential growth. At T2T-I we like to practice what we preach, so we’re first going to provide you with the definition from Dictionary.com: development at an increasingly rapid rate in proportion to the growing total number or size. Totally clear, right? But now we’re going to show you what exponential growth looks like using a real-world example.

In November 2014, Executive Director Chadd McGlone organized a conference for Guatemalan teachers in partnership with the nonprofit organization Common Hope. Twenty-five attended two afternoons of workshops on student-centered, culturally relevant teaching strategies. It was by all measures a success, but little did we know it was just the beginning.

In November 2015, the same conference was held again and grew from two days to three, six workshops to 34. The number of teachers participating was 256.

We now come to November of this year, with the conference adding one more day and nine more workshops. Most exciting, the number of Guatemalan presenters expanded from one to 15. That means that 70% of our workshop leaders felt empowered by our outreach to offer their expertise on topics ranging from understanding fractions to finding symmetry in nature to combining literacy with mathematics.

That sort of dramatic increase indicates that local teachers are taking ownership of and believing in the teaching strategies they are learning from T2T-I. And they are having fun doing it.

Guatemalan teachers sitting a tables with flowers and pinecones
Workshop participants in Antigua, Guatemala, explore Fibonacci sequences in nature

This picture at left illustrates one workshop led by two presenters from Guatemala City. The teachers are exploring Fibonacci sequences (where every number is the sum of the previous two) in nature using flowers and pinecones.

For 2017, the expected value of this equation will reach the national borders of Guatemala. Given that every region of this diverse country was represented at this year’s conference, we anticipate expanding even further in positive directions. In this picture, teachers are from El Parédon on the Pacific Coast, Alta Verapaz in the highlands, and the Lake Atitlán area nestled among the southern volcanoes.

Any student of mathematics can tell you that, while two points define a line, the third point confirms a definite upward trend. Where will the new points land? Stay in touch as we graph the excitement.

 

Thank you to Manuela Cea-Poblete, Guatemala Country Director, for her assistance in preparing this piece!

Their Own Words: Galápagos Math Team

From October 3 to 7, 2016, teachers in Galápagos had an opportunity to become students. Teams of experienced educators from at least six countries in North and South America offered lessons on best teaching practices for the subjects of mathematics and science. The following are reflections by three members of the math team. 

T2T-I thanks them for their contributions both in Galápagos and in putting their thoughts on paper upon their return home. We also thank Jonathan Drake for his stunning photographs.

 

From Monica Castro Wright, Math Teacher at the Colegio Menor San Francisco de Quito, Ecuador

This week was a great experience for me; teachers in Galápagos were, in general, more open to receiving ideas. I would love to do it again. I worked on project-based learning in mathematics, sharing the projects I have done with my students, which use Galápagos topics such as conservation.

Teachers worked in collaborative groups and discussed how to design projects for their math classes. We also discussed the importance of having students work in collaborative groups and explored the richness of using an interdisciplinary approach to mathematics learning.

By the end of the week, each group presented a design of their own creation to use in their classrooms, including a theme, a driving question, and an explanation of the math. I do feel that this type of workshop has an impact on the teachers.

 

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A pelican surveys the shoreline on Santa Cruz

 

From Beatriz Quintos, Professor of Education at the University of Maryland

Early Monday morning, with a high atmosphere mist, the bus picked up the teachers, and some taxis picked up the instructors. All of us instructors had been planning for months, and finally the time had come. Teachers split into two groups, some heading to a week of learning at Tomás de Berlanga school and others to El Colegio Galápagos.

Quickly we established a sense of community. It was essential for our team to create a safe, trusting environment to work towards the common goal: educating the Galápagos’ children. Teachers shared their expertise—an important element, because no one knows the Galapagos’ students and their families better. In order to create meaningful learning, we needed to connect math to students using real-life examples. Mathematics without a live context quickly becomes sterile and archaic.

Furthermore, children already have a wealth of knowledge. It is our role as educators to connect to it, draw upon it, and expand it, while simultaneously preserving its power. To that end, we engaged the Galapagueño teachers in role plays, simulations, problem-solving, and critical discussions about content and pedagogy. Together we imagined new ways of teaching, a different learning experience than most of us had. Anyone making this shift alone faces an insurmountable task; however, as a community we felt empowered.

 

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A blue-footed booby in mid-flight on Seymour Island

 

From Carolina Napp-Avelli, Professor of Education at the University of Maryland

The first thing we did was to spend a good hour or more just talking with the teachers, letting them introduce themselves, tell us what they teach, who their students are, etc. It was very important for me to start acknowledging who the teachers are and what they are concerned about. This conversation allowed us to later make connections between what we had planned and their concerns and experiences in their classrooms (such as students’ lack of motivation). We even changed some of the workshops we had planned to address some of their concerns.

I love to work with Teachers2Teachers-International, because I feel that my goal as part of T2T’s team is not to “dump knowledge” on the teachers but rather to develop a relationship with them — a true collaboration. I feel free to spend time on something like this that I consider important.

I think we may have made some impact in teachers with the workshops we have done, but I am convinced that just the workshops twice a year are insufficient to change teachers’ practice and beliefs. What I think will really make an impact is the combination of our workshops with the work that the coaches will do on a regular basis in between. I believe this is a crucial component of the program. It would be great to be able to keep working with the coaches throughout the year to develop a true collaboration:

  • discuss how the work she does relates to the work we have done in the workshops
  • share more materials and resources
  • get feedback from the teachers and the coach about what was more/less useful, what other needs they may have in terms of content and/or pedagogy
  • develop realistic and purposeful goals for the next round of professional development

I absolutely enjoyed the trip! Every second of it was super intense but super rewarding. I loved to work with the teachers, and I would love to go back and keep working with them. This has been an incredible experience for me.

 

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A lava lizard on Mosquera Island

Con permiso Santa Avelina

Elizabeth's selfie with elementary students

This post was contributed by Elizabeth Ollila (at right), who is currently a senior at Carrboro High School in North Carolina. T2T-I thanks her for participating on the 2016 Teacher Trip to Santa Avelina, Guatemala. Here are her words….

If only it were possible to explain to you the love, passion, and respect that travels through the streets and halls of Santa Avelina. Here’s a mental picture…

  • your host’s home has a kitchen stove that doubles as a counter for preparing food and where the children play and do homework
  • you sleep on a cot in a school, waking up to a shower that releases exactly five drips of an unpredictable temperature
  • you live in an ankle-length skirt for a week, which means teaching, playing soccer, and hiking to a waterfall, all in a sweaty, dusty skirt (while your hosts do the same and remain immaculate)
  • you stand outside of a school at 7:30AM to welcome all the students, knowing that most of them slept on hard beds shared among the entire family, some haven’t had breakfast, and others have already worked in the field

But along with all of this hardship, picture children with radiant smiles bigger than you have ever seen. Imagine the happiness on their faces as they line up first thing in the morning to get toothpaste from the teacher to brush their teeth. And their gratefulness during the morning break while they scoop their mugs into the big bucket of warm Mosh, a protein drink that provides many their only meal. Picture every kid greeting you with a buenos días as if you are the best thing in their day, while their teachers look so ready to make an impact.

Warm Welcome in Guatemala

Santa Avelina, Guatemala, is a community where everyone is welcome. Although I came with a team of strangers who clearly stood out, I was accepted with open arms. I could not walk down the street without children coming out of their homes asking me to play or just to scream a warm hello (laughing at my attempt to reply in Spanish). This community is poor, it has no medical care, and every piece of food is treasured, but I believe this community has learned how to thrive.

Santa Avelina is a place filled with simple brilliance that could be used in every part of the world. These people have close to nothing, yet they have done everything with it. They have created a school where the kindergarteners learn a second language, they are given responsibilities, high expectations, freedom and trust.

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Elizabeth with students at the William Botnan School, Santa Avelina

Highlights From the Heart

I know you have heard of poverty, and probably seen it too, but living in it at my age of 17 is life changing. Going back to my spoiled life seemed so unfair after my heart melted for these kids. These are my most vivid memories:

  • the cheerful chants of the six year olds as they entered their classroom
  • the crowd of kids that surrounded me during recess firing the question, ¿Vamos a jugar? (are we going to play?) over and over
  • the corn grinder beginning at 5:00AM to create the tortilla base for those who brought their own corn
  • the dog fights in the middle of the night and the chickens and pigs making noise at odd hours of the morning
  • the chunk of grassy dirt used as a soccer field by people of all ages with many games going on at once, not one with an actual soccer ball

Perspective Check

I went to Santa Avelina with the idea that we were going to live exactly like the community for a week, but how can I even claim we did that when a warm, delicious meal was never in question, when I had all my clothing from home, when my shower was guaranteed, when, in an emergency, we had a bus and money to leave, and when the circumstances were always temporary.

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Elizabeth and a local teacher prepare a lesson

An experience like this cannot help but change your view on everything around you. Being a part of Teachers2Teachers-International in Guatemala is not something I can explain to you. Instead, it is something you must experience. It has, in every way, made me a better person. It showed and reminded me of the simple things that are truly important in life. It showed me pain and struggle and made me realize stuff does not equal happiness. I was forced to see the world, and my country, in a new light, and to improve my global view.

Lessons Learned

I left Santa Avelina with so much more knowledge than I ever could have given. The people there taught me tradition, respect, love, simplicity, and brilliance in little things. They exemplified kindness and heart in everything they did, because they were neither afraid nor too proud to ask for help to improve their children’s future.

I was forced to remember that there is no difference between Edwin and me, or Marvin and me, or María and me, or anyone of those children and me. They did not choose their lives any more than I chose mine. I did nothing to deserve the luxurious, resource-filled life I live, and they did nothing to deserve theirs.

Santa Avelina gave me a desire to see the world as well as knowledge to help understand it. It showed me harsh reality and gave me the desire to change the struggles in the lives of those in poverty.

Hopeful Wishes

I can only hope that my limited knowledge, time, smile, attempt at Spanish, and (lack of) soccer skills made a difference in just a few kids’ or teachers’ lives. These people have the toughest lives I have ever witnessed, yet somehow they also have the softest smiles. While they are two airplane flights and a 12-hour, switch-back, bus ride away, I can’t imagine I won’t be back. Santa Avelina, you are forever in my heart.

Elizabeth and her mother in front of a waterfall
Elizabeth and her mother Mary, who is a public school math teacher, in front of the Santa Avelina waterfall

 

What does the title, Con permiso Santa Avelina, mean in English? In Guatemala, when you approach the door to another person’s house, classroom, etc, you ask con permiso to request permission to enter. The response of pase grants you entry.

 

Galápagos Goes Global

Written by Brittany Lenhart, T2T-I Intern, N.C., U.S.

How does a soon-to-be graduate of an International Education program finish up her degree in the best way possible? Let me share with you the answer: she travels to the Galápagos Islands to work with local teachers.

This past April, Galapagueño teachers participated in a five-day professional development institute organized by the Galápagos Conservancy. As an intern with Teachers2Teachers-International (T2T-I), I had an intimate view of everything that went on in the math subject area.

You probably won’t be surprised to hear that I consider this trip precious. Join me on this amazing adventure, as I try to recreate the experience.

 

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Upper elementary teachers celebrate after their workshop led by Arthur Powell and Lawrence Clark on Santa Cruz island in the Galápagos

Background

First of all, if you want to get a sense of what was accomplished during this trip, context is crucial. Historically, many local teachers are taught to teach using lectures and rote memorization, bypassing independent thought, active learning, or new approaches based on how young people learn.

We know for a fact that traditional teaching practices are widespread; however, further complicating innovative teacher training and professional development programs in the Galápagos Islands is their remote location.

Thanks to technological advances and the internet era, Galápagos is waving good-bye to their isolation and welcoming globalization with open arms. That’s how T2T-I enters the equation!

Team
T2T-I math advisory team members at Los Gemelos volcanic craters on Santa Cruz island in the Galápagos (Brittany is second from right)

Kickoff 

On the first day, the entire group of 130 teachers and 30 trainers gathered in the auditorium, where the amount of energy filling the room was really high. Part of the excitement came from the U.S. based teachers, who had spent months preparing for these workshops, and part of the excitement originated from the Ecuadorian teachers, who had been waiting, for years in some cases, for a chance to develop 21st-century classroom skills.

The project took off with the introduction of the U.S. based teachers, a survey for the Ecuadorian teachers and the agenda for the week.

Over the next five days it was my pleasure to assist in the delivery of multiple workshops with a number of presenters.

 

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Diego Roman leads a science workshop for teachers at the Tomás de Berlanga School on Santa Cruz island

Workshops

The first workshop I observed was led by two of the U.S. trainees: Tim Erickson, a retired math teacher, and Chadd McGlone, T2T-I Executive Director. During their presentation, they asked local high school mathematics teachers these questions:

What memories do you have of learning math in school?  

Is math something you do alone or together?

The trainers pointed out that in the world today, people collaborate all the time and everywhere. Being able to work with others on mathematical tasks is a skill that will benefit students in many ways.

During the opening activity, as the teachers sat in small groups of 4 or 5, they each received a piece of information about a math problem. For example, one teacher might know that the road was 20 km long, while another might learn that the bus can hold 35 students. In order to solve the problem, they had to work together.

 

math and science workshop scenes from Tomas de Berlanga School
Scenes from math and science workshops at the Tomás de Berlanga School, featuring Lawrence Clark, Diego Roman, and Arthur Powell (l to r)

 

When a group finished, Tim or Chadd would talk with them about the different strategies they could use when something like this happens in their classrooms. Tim offered this suggestion:

As the teacher, I can walk around the room and see what the groups are using, what strategies. This way, I don’t need to explain every strategy. I can ask a student to show another group the strategy they came up with. Students may benefit more from hearing the explanation from a fellow student.

The session ended with a discussion about applying in their own classrooms what they experienced about group work during the workshop.

Collaboration

Throughout the next four days the Ecuadorian teachers wholeheartedly engaged in the workshops, offering their perspectives and knowledge, asking questions, and trying out new learning tools. I am happy to say that by the final day of the workshops, I saw that collaboration was not just a word, it was a practice.

 

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Scenes from math workshops at the Tomás de Berlanga School, featuring Chadd McGlone, Tim Pope, and Lawrence Clark (l to r)

Building Relationships

As the week closed with another gathering of the entire group, I overheard many teachers offer invitations for the trainers to come back and continue their work together. I feel fortunate to be involved in this four-year project, because as exciting and monumental as this first installment was, its goals can only be reached with further collaboration. The relationships we built last week will be the springboard for this project to evolve into a real educational gem.

 

Image of 200 people in Puerto Ayora, Santa Cruz
Galápagos math and science teachers gather at the community center in Puerto Ayora, Santa Cruz

Let’s Eat (or Divide) Cake

Written by Kelley O’Brien, T2T-I Associate Director, Carrboro, N.C., U.S.

It was not until I was 20 years old that I learned to love math. This epiphany occurred during a game theory class I took from Professor Hollingsworth at University of Georgia (yes, I still remember his name). I discovered that math was everywhere, and that I was actually pretty skilled at using it. I think there are a lot of us, especially women, who believe we are “bad at math” until someone shows us differently.

 

Kelley O'Brien and Mary Ollila
T2T-I Associate Director Kelley O’Brien (left) and T2T-I team member Mary Ollila on their first trip to Guatemala, March 2016.

 

Imagine if those dreaded hours of math lectures were replaced with this: You walk into the classroom and your teacher has meticulously placed a “cake” made of blocks at the center of the room. As you take your seat, she entices you with this interactive story about a party.

She asks, “What type of cake shall we bake for our party? Chocolate?”

The class erupts in unison, “Chocolate!”

“What else do you want with the cake?” the teacher asks.

“Whipped cream! Caramel! Strawberries!” the class yells out in mouthwatering anticipation.

Your teacher tells you that this delicious cake we have baked, which is represented by blocks right in front of her, is divided into 20 pieces. You learn that there are twice as many boys as girls coming to the party, and each boy gets one piece of cake. There are half as many girls than boys coming to the party, and each girl gets two pieces of cake. The final detail is that the partygoers eat the entire cake.

Problem-Solving

“How many boys are at this party?” she queries. “How many girls?” You crowd around the blocks, moving them into servings of cake while complaining that girls eat too much. Then you figure out the answer to the question!

 

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First grade teacher and students at the New Hope School in Guatemala.

 

That’s the math I saw in a first grade classroom in Nueva Esperanza, a community north of Guatemala City. I could see that cake. I wanted to eat that cake. And, I’m sure that the six-year-olds by my side had the same thoughts. It was real and meaningful for them. How can you get more high stakes than chocolate cake topped with caramel, whipped cream, and strawberries?

Sticky Math

Most of all, this math lesson will stick, and not just because it included an imaginary concoction of gooeyness. These students learned that they are mathematicians. Something that I wish I had grasped long before I was 20 years old.

All the Knowledge Comes from Them

Written by Lucía Dávila, Guatemala City, Guatemala

So here I am with a group of Americans in a Guatemalan surf community, eating Italian pizza and discussing global education. Can you count how many cultures are involved in our lunch?

 

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Members of the Teachers2Teachers-International team relax over lunch in El Paredón, Guatemala

 

Last month, T2T-I had the opportunity to return to the community of El Paredón, Escuintla, on the Pacific Coast of Guatemala. Our team of six was excited to connect with the teachers and follow up with more professional development workshops.

Two of our team members had already visited the community in January, but for the rest of us everything was new. Let me be honest for a second, I am a proud Guatemalan aware of the cultural richness of my country; however, I’d never imagined we had a surf community within our borders.

I thought surfing was an Australian thing that had nothing to do with us. As it turns outs, I couldn’t be more wrong.

We were able to experience not only the characteristic warmth of the people living in El Paredón, but also the beauty of the natural landscape offered by Guatemala’s Pacific Coast. From footprints on black sand to a boat trip through the mangroves, we enjoyed many spectacular sights.

 

Activities in El Paredón
Walking on the beach at sunset, enjoying time around the table, boating through mangroves

Culturally Relevant Workshops

Because this was our second collaboration, the local teachers were familiar with our goals and schedule for the day. We worked with the pre-K and elementary teachers during the morning and with the middle school teachers during the afternoon.

We started with a relationship-building activity led by Katie Dutko, T2T-I Director of Education Programs. This allowed us to create connections and encouraged trust among the group. Next, Katie presented a workshop on contextualizing math problems, appreciating open questions, and finding different solutions to the same problem.

 

Teachers workshops El Paredón Guatemala
Workshops on math education with the teachers at El Paredón

 

Tim Quiroz, T2T-I team member, facilitated an activity using concrete, representational, and abstract sequences of instruction, while Chadd McGlone, T2T-I Executive Director, contributed with math patterns and the concepts behind them.

All the activities were supported by the use of games and manipulatives in a cultural context, while the teachers were encouraged to use sound mathematical reasoning to justify their thinking. Kelley O’Brien, T2T-I Associate Director, and Mary Ollila, T2T-I team member, joined in the activities to learn alongside the teachers.

Given that El Paredón is a seaside community, we explored numbers related to fishing.

Maybe T2T-I provided the overall structure of the task, but the knowledge came from the local teachers, who provided information about the different kinds of fish, prices, and appropriate terminology. We developed some engaging math activities and learned a lot about mathematics.

 

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Snapshots from two sessions of professional development

Teachers’ Feedback

During our feedback sessions, the local teachers expressed not only their gratitude but also what they had learned during the workshops. We were surprised and glad to hear answers involving more than math. Some examples were as follows:

  • “The kids will learn how to work in teams.”
  • “We are showing them to respect each other.”
  • “The students will know how to socialize.”
  • “The little kids will start to understand the dynamics of taking turns.”

We finished our work by giving professional development certificates to the teachers. Some of them even took extra certificates home! The teachers were so interested and eager to learn that some of them stayed throughout all the workshops, even ones pertaining to grades they didn’t teach. A teacher found the day so helpful that she asked us if she could bring colleagues from her district to the next one. Hopefully, we will be able to see new faces on our next visit!

 

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Proud participants display their well-earned certificates