Teacher resources and professional development across the curriculum

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Music in Math

mathoftimeMarch is almost over and so is Music in our Schools Month. We finish this set of Monday Motivations on music by looking at how to incorporate music into the math classroom.

High school and college students can study how the Greeks applied mathematical thought to the study of music in the video and online text for Mathematics Illuminated, unit 10, “Harmonious Math,” section 2, The Math of Time.  Section 3, Sound and Waves, looks at how sound waves move through the air and section 6, Can You Hear the Shape of a Drum?, asks if it’s possible to deduce what object makes a sound based on the frequency content of the sound.

In Memory of Chinua Achebe

achebeThe world lost an important voice with Chinua Achebe’s death. Critics consider the writer, born in Ogidi, Nigeria in 1930, one of the finest Nigerian novelists. Chinua Achebe eschewed trends in English literature and wrote by embracing the African oral tradition. (See the Chinua Achebe biography page from In Search of the Novel, Ten Novelists, for background on the author and his writing style.  The Ten Novels page provides a synopsis and reviews of Things Fall Apart.)

Achebe’s novel Things Fall Apart asks readers to consider, that while people often resist change, what if  their whole way of living was suddenly threatened by a group of outsiders? Okonkwo, the protagonist of this work, faces the imminent influence of British values on his Nigerian community.

Anthony Appiah, Achebe’s friend, explains his view of the novel Things Fall Apart in the program Invitation to World Literature: “One of the things that Achebe has always said, is that part of what he thought the task of the novel was, was to create a usable past. Trying to give people a richly textured picture of what happened, not a sort of monotone bad Europeans, noble Africans, but a complicated picture in which mistakes are made on both sides.”

In Teaching Multicultural Literature, workshop 8, “Social Justice and Action,” author Joseph Bruchac talks about his friendship with Achebe and how Achebe influenced his writing. He says:

“I asked Chinua why he wrote that novel (Things Fall Apart). He said that when he was in college, he was forced to read a book called Mr. Johnson by an English writer named Joyce Cary. In that book, which takes place among the Ibo people, Mr. Johnson is a pathetic figure, an Ibo man who wants to be like an Englishman but can never achieve that level. He dresses like an Englishman, tries to walk and talk and act like an Englishman. And he fails utterly.

And Ibo culture is just a background of this, is seen as savage and dirty and primitive and of little worth. Chinua said, ‘I had to write Things Fall Apart. To represent my people as they really are. As full human beings.’ Not perfect, because his main character has a tragic flaw. But ‘as full human beings in their own right.’”

 

Are you smarter than a Harvard graduate?

privateuniverseHarvardgrad

What causes seasons? Do you think you know? A common answer among school children and college graduates is that seasons are caused by how close the Earth is to the sun, but this answer is not correct. The tilt of the Earth’s axis causes the cycle of the seasons. See an explanation in Science in Focus: Shedding Light, workshop 7.

A Private Universe

More than 23 years ago, video producers asked new Harvard graduates and 9th grade students at a nearby high school some basic science questions, including “What causes seasons?”, and got surprising answers. That footage became A Private Universe, a documentary that looks at how students’ misconceptions block learning. The program looks at celestial movements, the seasons, and how these are taught in school.

In the program, a bright 9th grader named Heather is asked to describe the orbit of the Earth and explain what causes the phases of the moon. Her strange drawing of the orbit leaves her teacher perplexed. Also, Heather is only able to correctly explain the phases of the moon by picking up physical objects and using them to show her thinking. (You can see what became of Heather in the film A Private Universe, 20 Years Later.) Heather’s teacher learned two lessons by observing her explanations: 1. She can’t make assumptions about what students know already. 2. Using manipulatives (like balls to show orbiting planets) is important for understanding scientific concepts.

Where do students’ private theories come from?

Sometimes misconceptions are caused by misleading diagrams and drawings in textbooks that are interpreted or remembered incorrectly. Sometimes the concepts were taught incorrectly. Sometimes students hear words used in one context and apply their understanding to other contexts. Many times, children rely on their experiences, which can limit understanding. Even the brightest students can have trouble with basic concepts, because new ideas are competing with previous knowledge. In addition, teachers are required to cover a lot of material quickly and often don’t have time to tease out these misconceptions.

How can teachers help students?

First figure out what students know about a topic. Anticipate and address any misconceptions that might hinder learning new and related concepts. The three Essential Science for Teachers series include a section called “Children’s Ideas.” Using research on what children believe about basic science concepts, teachers are asked to consider what misconceptions children might have about these concepts and where these ideas might have come from. For example, Earth and Space Science, session 1, considers children’s ideas about soil.

Here is a list of resources from the Essential Science for Teachers series to help you examine children’s ideas in science:

Earth and Space Science

Life Science

Physical Science

Addressing misconceptions is important in all subject areas, not just science. While teaching Spanish at the high school level, I first took for granted that my students understood the parts of speech and learned that many did not. I often hear Africa referred to as a country and that Spanish is the official language of Brazil. Even as adults, we can hold misconceptions somehow learned along the way.

Before you start your next lesson or unit, try to anticipate and address any misconceptions and access prior knowledge. Then build from those ideas while giving students many hands-on opportunities (especially in science and math) to explain their ideas.

What surprising misconceptions have you witnessed in your classes?

 

Because I Had to Teach It…

handraisediconMovies and books are full of heroic teachers who face up to institutionalized rules, rigor, and rote learning that steamroll students’ thinking and their own inventive instructional methods (Robin Williams in Dead Poets Society). The counter stereotype is the teacher who has been beaten down by “the system,” sticks to the same syllabus year in and out, and basically puts the students to sleep (Ben Stein in Ferris Bueller’s Day Off and Professor Binns, the ghost who teaches the History of Magic at Hogwarts).

The teachers you don’t hear much about are the ones who are spurred to research a topic because a student asks a question they don’t know the answer to. These teachers are honest enough to look at what they don’t actually know and then go learn about it.

Kerry Emanuel, professor of atmospheric science at MIT, was driven to look into the energy systems that feed hurricanes as a result of having to teach a course in tropical meteorology.  “… one of the reasons that teaching and research go together so well is that, often, you think you understand something. And it’s not until you have to teach it that you understand that you don’t understand it..,” Emanuel explains in the program “Atmosphere” from The Habitable Planet.

Many teachers find themselves in the same position in K-12 classrooms. Whether you’re a teacher who has had an economics course dropped into your lap by your department chair – “Here are the tests and worksheets from the last guy who taught it.” —  or you have to answer a particularly probing question from a student, the feeling is mighty uncomfortable.  Do you stay up late reading the textbook, go to YouTube, or what?

Heather's classroom

Heather’s classroom

Economics teacher, Heather Anderson, took a practical view of taking on a course in a new area. “The only way I could move [to her current school] was to teach world history and economics. And I thought, ‘I can do it. I’ll get through a couple of years and then I’ll get rid of the economics and I’ll be left with the world history.”  Heather shifted the effort to the students and brought into her classroom simulations on market forces and supply and demand, rather than lecturing. By holding buying and selling markets in her class, her students could experience how these concepts worked in a restricted situation, like conducting research. Start at 28:30 of the video for The Economics Classroom, workshop 3, “The Government’s Hand.”

Another challenge for teachers is generating student ideas and making use of ideas that may be wildly off course, but are based on rational thinking. Audrey, a seventh grade social studies teacher, was assigned a science class with little formal science background. She focused on developing her students’ critical thinking skills so she could explore the science concepts along with them. Audrey started her research by conferring with a science education professor who helped her shape lessons around her teaching goal. See Case Studies in Science Education, program 25, for the full video.

Audrey's classroom

Audrey’s classroom

As these teachers (and many others) can attest, it takes a lot of effort to get the students to do their own thinking and to stay with them (or just slightly ahead of them) as they work through their ideas.  Throughout learner.org, teachers discuss how they have learned more effective ways of teaching from listening closely to student questions, observing their thinking, and getting input from the whole class. You can also use the search function on learner.org to do research on new topics in the subject area you are teaching or will be teaching.

Do you have a story about a question from a student that sent you off to learn more about your subject?  Or do you do research on your own?  Share it with us and your fellow LearnerLog readers.

Música, Musique, Musik

“Music is the universal language of mankind.”

— Henry Wadsworth Longfellow

TFL_French_ZydecoMarch is Music in Our Schools Month and educators are urged to make a case for including music education in the K-12 curriculum. It would seem to be an easy argument. According to Christopher Viereck, Ph.d., Developmental Neurobiologist in Residence for The Music Empowers Foundation, ongoing music education creates “new connections (‘wiring’) between brain cells.” Music education “also benefits students in other academic domains,” writes Viereck in Music Education and Brain Plasticity 101, the first of many articles in the Your Brain on Music Education series.

Still, despite the substantial amount of evidence that supports the claim that music enhances learning, music programs in budget-strapped schools are often considered niceties, not necessities. There are ways to incorporate music into lessons, should formal music programs face the axe, however. Take foreign languages, for example.

The Teaching Foreign Languages K-12 video library provides two examples of how to incorporate music into language lessons. Watch French: A Cajun Folktale and Zydeco. At about 20 minutes into the video, students are introduced to Cajun music. See how the teacher builds excitement for what students will be learning and how music helps students better understand cultural traditions of the people who live in that particular region of Louisiana.

Music can take students from the Bayou to Ancient Rome. In this mixed-level Latin class at Westfield High School in Chantilly, Va., teacher Lauri Dabbieri uses music to help students understand the difference between translation and interpretation, as well as to make historical connections to Roman culture.

How else might you use music in your foreign language classroom?

 

Where in the World: A Story of a Geologist’s Ingenuity

Do you know where this is? Both pictures are of the same island. The first photo shows a normal, peaceful day and the second shows a volcanic eruption that threatened this bustling fishing harbor. Follow this link to Power of Place, program 6, “Challenges in the Hinterlands,” for an amazing story of a geologist’s ingenuity that saved the harbor. (see 19:16 to 21:06 in the video)

Power of Place_IcelandBoat

Power of place_IcelandEruption

 

 

 

 

 

 

 

Expanding Girls’ Horizons in Science & Engineering Month: Astronomer Vera Cooper Rubin Persists

Physics_rubinWhat keeps scientists like Vera Cooper Rubin moving forward when the obstacles in her way are insurmountable by others? Born in 1928, Rubin faced educational limitations set on women during her time: a high school teacher who discouraged her from pursuing science, Princeton’s then policy not to accept women into astronomy programs, and skeptical peers in the science field. But she persisted in her work and gained reputable recognition as an astronomer.

In the 1970s, Rubin and collaborator Kent Ford made a significant discovery in physics. They measured the rotational velocities (how fast they spin) of interstellar matter in orbit around the center of the nearby Andromeda galaxy. Then they compared these studies with those of other galaxies and were able to infer that the galaxies must contain dark matter.

Read how Rubin and Ford arrived at their conclusion and what that meant for understanding dark matter in Physics for the 21st Century, unit 10, section 2, Initial Evidence of Dark Matter. And if you teach students who are curious about science, use Rubin’s story to encourage them to follow their interests. One of them might end up solving the mystery of dark matter altogether.

Healing the Injured Brain

Neuroscence_5_brainWe’ve got brains, but how much do we really know about them? March is the perfect time to learn more about this amazing organ because we have Brain Awareness Week (March 11-17) and Brain Injury Awareness Month. The public is encouraged to learn how to develop a better understanding of the brain and its functions, and combat the stigma of brain disorders through education.

Educators have long been interested in understanding the brain, and many professional development workshops have encouraged K-12 teachers and administrators to create learning experiences that provide for the vast differences in the way each student learns.

Still, for as much as we think we know about the brain—about what functions are housed in the left side or the right side of the brain, for example—along comes that exception to the rule that forces us to reconsider our conclusions. In unit 1, section 4 of Neuroscience & the Classroom: Making Connections, we are asked to consider this question:

If the two hemispheres [of the brain] are heavily involved in virtually everything we do, what happens when one hemisphere is removed?

Nico’s Story and Brooke’s Story answer this question. (Watch the short case study videos on the Neuroscience page.) These are two very different young men, yet they have much in common. Their stories support the assertion that environment affects learning. Think about how the attitudes of family members and teachers help the boys succeed and how these stories inform teaching.

 Brain Injury from Accidents

The brain’s ability to function as it should is affected by many things. For Nico and Brooke, a physical disorder forced a permanent, structural alteration of their brains. Those kinds of drastic surgeries are rare, however. Most of the time, the brain’s function is altered by accident. A bump, blow, or jolt to the head can cause a traumatic brain injury (TMI). The Brain Injury Association of America estimates that 1.7 million people will sustain a brain injury each year. Furthermore, according to the Centers for Disease Control (CDC), sports concussions in the United States have reached an epidemic level.

Brain injuries can result in physical, cognitive, and behavior challenges. Getting immediate treatment can make a big difference in long-term quality of life. The Brain: Teaching Modules, program 32, “Neurorehabilitation,” shows case studies of people who have overcome their brain injuries thanks to early treatments. For example, five minutes into the video, you’ll meet Thais, a 16-year old junior in high school. She describes the reaction of her peers to the non-visible symptoms of her brain injury caused by an automobile accident. This straight-A student suffered speech and language problems as well as memory loss. How might teachers help students better understand the nature of brain injuries and support students who suffer and survive injury to the brain?

For additional resources on the brain, how it functions, and how knowledge of the brain informs classroom instruction, search “brain” at Learner.org.

Use Music to Teach Social Studies

bio of america_23_elvisHow can you use music to enhance your social studies lessons? Here are some ideas:

1. The Middle Ages: Early music provides an echo of the past, allowing students to connect to people, cultures, and arts from long ago. Using The Middle Ages interactive, students test their ears by determining which of the instruments used by medieval musicians match the sounds they hear.

2. The Renaissance: Elementary music specialist Sylvia Bookhardt teaches students about Renaissance society in The Arts in Every Classroom,Teaching Music.”

3. The Holocaust: The series TeachingThe Children of Willesden Lane’ offers resources to help middle and high school students better comprehend survivor Lisa Jura’s story of loss, resilience, and ultimate triumph. Mona Golabek, Jura’s daughter, wrote The Children of Willesden Lane to honor her mother, who was spared the cruelty of the death camps thanks to the Kindertransport (children’s transport). In all, the operation saved nearly 10,000 children. Music played a central role in Lisa Jura’s life and is integrated into this memoir. Find the music downloads here.

4. The Fifties: Explore an emerging American teenage culture, including the influence of the transistor radio and a young man named Elvis Presley, in A Biography of America, unit 23, “The Fifties.”

Expanding Girls’ Horizons in Science & Engineering Month: Lene Hau Stops Light

Physics_7_Hau_labHave you seen the AT&T 4g network ad in which a friendly guy in a suit asks a group of young children, “What’s better, faster or slower?” The children sing out “Faster!” and give examples of things that are fast: “my mom’s car,” “a space ship,” “a cheetah.” None of them mentions light, which travels close to 200,000 miles per hour. Anything that moves that fast has to be unstoppable, right? Wrong. Superman could stop a speeding train, but it took a super woman to stop light.

Before I get to physicist Lene Hau’s story, let’s ask why anyone would want to stop light. While the process of slowing or stopping light is incredibly complex and precise, the reason for doing so is quite simple. Light can carry a lot of information very quickly. If you can pack light with gigantic collections of information and route it to super computers, you can process more data—solve more problems—more quickly than with the puny computers we use today.

While Physics for the 21st Century is designed to explore the frontiers of modern physics, unit 7, Manipulating Light, is also a testament to the profound contributions that women are making to science. Dr. Lene Hau, recipient of a MacArthur Fellowship “genius grant,” stopped light by ignoring skeptical colleagues, by using science and mathematics to tame the weird world of quantum mechanics, and by relentlessly pursuing her goal. She is one of two featured scientists in the unit 7 video. Also, see her talk about the process of slowing down light in this video from the Harvard YouTube channel.

Physics_7_Hau_signDr. Hau never stopped calculating:

“I remember I was taking off in the airplane from Boston to Copenhagen and following the speed of the airplane on the big screen there and thinking, oh, wow; now we are going faster than my light pulse in the lab. I was calculating if I had sent a light pulse from Boston at the time I left in the airplane I would arrive in Copenhagen an hour before my light pulse.”

And she reveled in the wonder of her accomplishment:

“. . . in the middle of the night and you were just sitting there and you’re just the first person in history being in this regime of nature seeing light go this slow. It was really amazing . . .”

To make her breakthroughs—first to slow light to “bicycle speed” and then to stop it altogether—Dr. Hau lived in a world of both absolutes and mystery. Her team put the fastest known thing into the coldest known thing. Light, at billionths of a degree above absolute zero, stops. Essentially, Dr. Hau and her team were manipulating light and atoms so that they share characteristics that they don’t appear to have in common in the non-quantum world. A mile-long pulse of light is compressed to .02 millimeters (less than half the width of a hair) and sent through a Bose-Einstein condensate, a super cold cloud of sodium atoms. When the light is slowed, the information carried by the light can be imprinted in the sodium matter.

Even though Dr. Hau was manipulating light in the miniscule, sub-atomic world, she never thought small or shied from taking risks:

“If you want to probe something, probe it as hard as you possibly can without it totally blowing apart.”

We are still some years away from seeing Dr. Hau’s amazing work being put to practical use in quantum computing and other still-unknown applications, but now is just the right time to applaud her and join her in imagining where she will take us from here. Use her story to inspire your students to pursue exciting work in the sciences.