Math Class is Tough!

I remember the commotion started by Teen Talk Barbie when she announced, “Math class is tough!” in the early nineties.  After only a few months, the phrase was taken out of the dolls’ vocabularies and Mattel swapped out the dolls that still said the phrase.  These toys echoed a much larger cultural trend that continues to plague math teachers across the country: being smart and doing well in math doesn’t always make you popular.  Social conditioning can lead students, especially those in their very impressionable adolescent years, to believe that math is very hard and “uncool,” and generally not worth their time and effort.  It’s often seen as a required subject to pass, not a subject that will be interesting, fun, and ultimately very useful in life.  Making math accessible and intriguing and even cool to these students is an obstacle that successful math teachers overcome.  Math class can be tough, but students who enjoy it from a young age will enjoy it enough to make it worth the effort.

Great middle school and high school math teachers find ways to connect with their students to help them embrace and enjoy math, blending mathematical concepts into all different subjects. Integrating subjects like this can seem like a lofty goal for those of us who are constantly short on time, but there are plenty of Gateway resources to help you out.  If you start a search for math resources, you can narrow your search with a secondary subject (such as art). When I did this search, I found a neat lesson about M.C. Escher artwork and the mathematical concept of tessellations.

You can intrigue your students by presenting real-world projects and activities that demonstrate the relevance of math in students’ lives.  Tessellations and fractals are both math concepts can be taught with fun hands-on activities at many grade levels.  Many adolescent students will balk at a discussion of interior and exterior angles, and how different geometric shapes can fit together.  These same students might truly enjoy exploring the concept with manipulatives or interactive computer models.  From simple pattern-building activities in the primary grades to some of the more complex activities available on the Gateway, using hands-on activities and visual aids is appealing and memorable to many students.

My favorite math and science teachers showed me how to embrace my inner “nerd,” helping me succeed in math despite the social pressure (and Barbie) telling me that math class is tough. In my calculus class, the community was so tight-knit that we created a class shirt that was actually cool to wear it around campus.  In that classroom, I learned an important lesson: being a dork or geek is not a bad thing!  In her book Math Doesn’t Suck, Danica McKellar takes an opposite approach by showing teen girls that math is actually cooler than they think, and not just a subject for the smart boys. The Wonder Years actress turned math guru’s books are a good resource to suggest to girls struggling (or not trying) in your class. 

As a math teacher, you are a very important role model for your students. Your love for math will show, and if you get excited about math in your everyday life, your students will notice.  If you have fun and embrace your own inner “geek,” maybe they will, too. Kids who learn to love math today will excel in it tomorrow. Good luck, and please let us know if you have successful math activities you want to share.


~Peggy's Corner - 9/1/2011~

Repeat After Me….

It’s always fun to do something unexpected in the classroom, and to watch the kids’ reactions. It’s especially gratifying when the event furthers a curricular goal, or makes subject matter more palatable to the students.  I remember one day in middle school where we math students weren’t particularly engaged in the material, and the teacher’s attempts to salvage the class weren’t working. She was a fine teacher, and we were normally motivated learners, but it was just one of those days where things didn’t click. She sighed, scrapped the lesson, and took out a large book of M.C. Escher drawings. While most of the students had seen some of his work before, the tessellation pictures were the ones we focused on. We marveled at the intricacy and precision of his work, and before long were discussing different types of symmetry and what types of shapes could and couldn’t be used to produce tessellations. It wasn’t the lesson the teacher had originally intended (or even wanted) to teach, but she did what gifted educators everywhere do: she took the class pulse, decided to change tactics by introducing something novel to the class, and wound up still delivering math content in a way that was memorable and valuable. 

Tessellations are neat things. They’re created when a specific shape is multiplied and repeated over and over, until it covers the entire surface of a plane without any gaps in the pattern. Tessellations are sometimes also known as “tiling,” and can occur in nature as well as being a man-made product. The repeated shapes shown on brick walls, soccer balls, honeycombs, and the sections of an orange, for instance, are all examples of tiling, or tessellations. The use of tessellations as a decorative motif has been traced to the ancient Sumerians, who some 4,000 years ago decorated the walls of temples and other buildings with elaborate repeated patterns. It’s a fine blending of mathematics and visual art – a fairly rare combination – and can be a great topic to engage students who usually don’t like math. The trick is to consistently emphasize the mathematical properties of tessellations, and how they in turn make the artistic properties possible.

Tessellations can be taught across the curriculum and to a variety of age groups. Younger students can use pattern activity blocks to emphasize patterns and symmetry while working on their problem-solving skills. Older students can calculate distance using individual tile measurements, explore the different types of symmetry on a plane, and figure out which shapes tessellate and which ones don’t. All ages can create their own tessellations, using either simple shapes like triangles and squares or more complex irregular shapes. Tessellations can be studied in the art classroom, and in science by examining symmetry in nature, such as in animals and plants.

This week I’ve highlighted three hands-on tessellation lessons with activities for a variety of ages.  Please be sure to read Peggy’s companion column where she discusses how to use these resources and others in the classroom. We’ll also be featuring several new lessons and resources on this topic each day throughout the week on our Facebook and Twitter pages, so be sure to take a look.

Exploring Tessellations

http://www.thegateway.org/browse/dcrecord.2011-08-24.6118809390

Subjects: Geometry, Art

Grade: K-2

In these activities, students learn about tessellations and how to create them. They learn to tessellate with one shape, two shapes, and finally with three dimensional (3-D) shapes. This lesson was produced by the Geometry Playground at Exploratorium, a museum of science, art, and human perception located in San Francisco, California. The Exploratorium offers a host of materials for educators, including lesson plans.

Medieval Tessellations

http://www.thegateway.org/browse/dcrecord.2011-08-24.0009022082

Subjects: Geometry, Art, World history

Grade: 6-8

The major focus of this lesson is to surreptitiously introduce the teaching of math concepts across the curriculum. Students will each produce a tessellation of original design that effectively uses shape, pattern/repetition and color to create a "beastie" inspired by bestiaries of the Middle Ages. This lesson is a produce of the Incredible Art Department at Princeton Online, and offers a plethora of materials for art teachers, art students, parents, homeschoolers and artists.

Let’s Tessellate

http://www.thegateway.org/browse/dcrecord.2008-05-01.5810723795

Grade: 9-12

This lesson is a hands-on, technology-based project that will take place in the classroom and computer lab. Students will discover which regular polygons tessellate the plane by constructing polygonal tessellations. Students will also use a spreadsheet to calculate the area and perimeter of the polygons. This lesson was produced by the Alabama Learning Exchange (ALEX), an education portal that provides lesson plans, education-related podcasts, best practices, and Alabama professional development activities. Lessons are aligned to Alabama Content Standards.

~Joann's Picks - 9/1/2011~ 

Connecting the Dots

Over the past 100 years or so, stars seem to have disappeared from daily life. Our ancestors didn’t take the stars for granted; for them, the night sky often served as compass, clock, calendar, and a rich source of inspiration for tales of mystery and wonder. Skyscrapers and light pollution have dimmed the brilliance of the night sky for many of us in the 21st century, but for those who happen to stop for a bit and look upward, the sky’s glittering patterns are still there for the gazing.

The constellations that appear nightly in our skies are the same ones that our ancestors have viewed for millions of years. Constellations are groups of stars that appear to form patterns in the sky, and that can be perceived as figures or designs. In an attempt to better understand the vast world around them, ancient civilizations named and assigned stories to the constellations, many of which are still noted today. Many of the constellations’ names and stories are derived from classical mythology, which makes them a wonderful topic for teaching across the curriculum. Science classes, of course, can easily incorporate the study of constellations into a regular astronomy unit. English and language arts classes can take advantage of students’ enduring love of the Percy Jackson series to learn more about the stories behind the constellations, and perhaps create their own constellation myths. Social studies classes can discuss the importance of constellations to civilizations throughout history, and how various cultures assigned different interpretations to the same star or groups of stars, and which reflected their cultural beliefs and customs.

The viewing of constellations requires no special equipment, just a swath of night sky, a marked star map or guide, and some patience. If cloudy skies or light pollution obscure your night viewing, online alternatives are available and great tools for classroom use. At this point, the only constellation that I can reliably identify is Orion, the Hunter, but I’ve vowed to learn at least several more by the end of summer. Finding constellations can be a remarkably powerful experience, and a way to remind ourselves that despite our frenzied and full lives, we’re still all part of something much larger and grander than ourselves.

This week, I’m featuring three resources on constellations for different grade ranges, and will be highlighting many more resources on this topic throughout the week on our Facebook and Twitter pages. Please be sure to join us.

Glowing Constellations
http://www.thegateway.org/browse/dcrecord.2011-03-07.7495089943
Subjects: Art, Astronomy, Language Arts
Grade: K-3
Students choose and research a constellation, then use pictures to help design an accurate bas-relief replica of the constellation. This lesson was produced by Crayola, maker of art supplies. Crayola also offers lesson plans, an online certificate maker, and other resources for educators.

Constellations
http://www.thegateway.org/browse/dcrecord.2011-03-07.8638643557
Subjects: Mythology, Astronomy
Grade: 3-8
In this lesson, students will "connect the dots" to form constellations from stars, recognize some famous constellations and the myths behind them, and compare their perspectives to the perspectives of other students and ancient peoples. This lesson is offered by the Sloan Digital Sky Server (SDSS), a project that uses current data to make a map of a large part of the universe. In addition to offering data for astronomers, SDSS also offers educational resources and games for teachers and students.

~Joann's Picks - 3/18/2011~

Constellations in Science and Mythology
http://www.thegateway.org/browse/dcrecord.2011-03-09.9458287248
Subjects: Art, Writing, Astronomy
Grade: 9-12
This project requires students to research constellations and produce illustrated books suitable for third to fifth grade readers. The books must include the story and mythology behind the constellation, information about the two brightest stars in the constellation, and Messier objects found in the constellation. This lesson was created by Debbie Scheinberg, a high school science teacher at Cherokee High School South in Marlton, New Jersey.

Revolution Solution?

Over the past few weeks, the world has watched while Egypt has been in the throes of a revolution. The story of a country beset by repression, poverty, and civil unrest, and ruled over by an immensely wealthy and out-of-touch leader, is not new. In fact, it’s a scenario that has occurred repeatedly throughout the centuries, and is likely fated to play again in the future.

In the early 20th century, Russia was a vast country with the third largest population in the world. Although the major urban areas were centers of rapid industrialization, much of the country was still an agrarian society where workers toiled under primitive conditions. The Russian people, too, were diverse, with great disparity in their economic, religious, and cultural situations. Presiding over the country was the middle-aged Imperial Czar, Nicholas II of the House of Romanov. The Romanovs had ruled Russia since 1613, but by all accounts (including his own), Nicholas had not been adequately prepared for the rigors of running a country. His reign continued a cycle of national repression, high taxes, food shortages, labor strikes, and deplorable working conditions, all of which contributed to growing public discontent, and anger towards the monarchy.

The Russian Revolution is often viewed as a sudden, climactic event, culminating with the brutal assassination of Czar Nicholas II and his family. In reality, the revolution occurred in stages, with long periods of civil unrest, repression, and public protests. Ultimately acknowledged as a kind and religious man by those who knew him, Czar Nicholas was nonetheless an ineffectual leader and uninspired politician. His country in shambles, he retreated to his palaces and a life of unimagined luxury. To critics of the czar, the famous jeweled Easter eggs created for the Romanov family by Fabergé came to symbolize the monarchy in their opulence, privilege, and utter uselessness. Forced to abdicate his throne during the first part of the Revolution in February of 1917, Czar Nicholas and his family were gunned down later that year by Bolsheviks, thus definitively ending the imperial era in Russia and casting the country into civil war. Preferring style over substance, and completely out of step with the needs of their country, the Romanov story is ultimately a tragic one.

The Russian Revolution was a pivotal event not only in Russian history, but for the world at large as well. Decades later, the Bolsheviks morphed into the Communist Party of the Soviet Union, which lasted until the late twentieth century and whose political philosophies still guide some countries today. My picks this week focus on the Russian Revolution and the end of Imperial Russia, and the dichotomy between two very different worlds. Throughout the week, I’ll be featuring many additional resources on this topic on our Facebook and Twitter pages, so be sure to check those as well.

Russian Imperial Eggs
http://www.thegateway.org/browse/dcrecord.2011-02-01.2652725425
Subjects: Art, World History
Grade: PreK-5
This lesson introduces young students to Imperial Russia in the early 20th century. Each Easter, Nicholas II, the last czar of the Russian empire, gave his wife and mother each splendid jeweled eggs. Students will learn about the royal family’s Easter tradition (but not the family’s ultimate fate), and create their own jeweled eggs crafted in the style of Fabergé. This lesson was produced by Crayola, makers of the ubiquitous art supplies. Crayola also offers lesson plans, an online certificate maker, and other resources for educators.

The Russian Revolution
http://www.thegateway.org/browse/dcrecord.2011-02-01.7062497715
Subjects: Geography, World History, Government
Grade: 7
In this lesson, students explore the events leading up to the Russian Revolution using online video clips and activities. Students also research the geographical and cultural effects of Russia’s expansion, and discover why the country entered a near-regressionist state as it emerged from absolute monarchy to communist state. This lesson was produced by the Core Knowledge Foundation, a nonprofit and nonpartisan organization that develops curricula, provides professional development for educators, and publishes educational books and other materials.

The Faberge Eggs: Mementos of a Doomed Dynasty
http://www.thegateway.org/browse/dcrecord.2011-02-01.0869347570
Subjects: English, Art, World history
Grade: 9-12
What to the things we treasure tell us about ourselves and the culture in which we live? The significance of the Fabergé eggs can be interpreted in several ways. They can be appreciated for their fine craftsmanship and for the family memories they represented to the Romanovs. On the other hand, their fragility and extravagance can symbolize that family's world of insular, imperial privilege. In this lesson, students will create an exhibition of items treasured by their families and reflect on the personal and cultural significance of these items. The exhibition process can be divided into Social Studies, Visual Arts and Language Arts lessons, either by working with the teachers of each of those subject areas or by teaching as one unit. This lesson was produced by PBS Treasures, a series of videos and lesson plans that examine the stories behind masterworks of art and nature.

~Joann's Picks - 2/18/2011~

Renaissance Students

Do you have a polymath in any of your classes? A what?? A polymath is defined as a very learned person with encyclopedic knowledge. A polymath is a person who thinks, explores, and experiments to become an expert in many fields. These are the kind of people who treasure lifelong learning (and people you definitely don’t want to go up against in Jeopardy!). I know I don’t quite fit into this group of experts, although I wish I could say I do. To create a thinker of this caliber is the ultimate goal of many educators.

In an ideal world, students would have an insatiable hunger to learn about the world around them. Teachers would simply be there to guide their learning and provide the resources students need to fulfill their curiosity. The study of art could lead to learning about science. Inquisitiveness could lead to new inventions and discoveries. Unfortunately, it doesn’t always work that way, and it is up to parents and educators to bring the love of learning and exploring new idea to their students so they will have the desire to continue fulfilling their curiosities throughout their lives.

There have been some great renaissance men and women throughout history, and Leonardo da Vinci is a perfect example whose life has been prominent in recent books and movies. Thinking about successful historical figures like da Vinci made me wonder what we can do as teachers to inspire students to embrace learning enough to become well rounded and learned like these people. After all, according to Leon Battista Alberti, “A man can do all things if he will.” How can we encourage this will to do new things?

Although studying the life and learning of da Vinci in your classroom probably won’t create a classroom full of polymaths or renaissance students, it might inspire students to think about the amazing things they could do with their lives. It can also serve as a great theme to tie together lessons from fields including art, science, and math. A perfect example of studying a variety of fields under the umbrella of one theme can be found in the yearly studies and competitions of Academic Decathlon teams. I’ll discuss that more in future columns, but it’s an idea to look into if you work with high school kids.

Math might seem a lot more interesting to students when it is presented within the theme of Leonardo da Vinci’s artwork. Drawing in perspective can be a lot more relevant to students when they can see how it has been done throughout history. There are a lot of well-made lessons on The Gateway to help you bring Leonardo da Vinci and his discoveries and studies into your classroom. The Boston Museum of Science did a wonderful job creating a science-based approach to studying the life and times of da Vinci. Browse through their site to see some ideas for incorporating this theme into your teaching. The lessons were designed for 4th through 8th grade students, but are adaptable to many levels. Here is a sample of what the Museum of Science has to offer:

Inventor’s Toolbox: An interactive site to explore the elements of simple machines with a game using three simple machines. This activity can be done online or as a classroom activity

Using Leonardo’s Window: A lesson in creating proper perspective in a drawing using a Renaissance technique of drawing a scene on a glass window.


How Far? How Small? A measurement activity where students measure the change of the apparent size of an object as it moves away from them.


Leonardo: Right to Left : An activity for students to experiment with writing in reverse.

~Peggy's Corner - February 4, 2010~

Digging Deeper into the First Thanksgiving

Thanksgiving in America is a time for students and teachers to take a little break from school to reflect on the history of our country and to give thanks for all that we have. For many, it’s a time to take a vacation where we eat WAY too much and get up at crazy hours of the morning to get a head start on the Christmas shopping! In an attempt to help students understand the origin and the meaning of the holiday, many teachers teach Thanksgiving lessons during the time before the holiday. Some teachers choose to focus on the gratitude associated with the season, hoping to instill some of that thankfulness in their students. Other teachers choose to focus more on the historical events in the United States that inspired the holiday. Interactive internet resources can bring the classic study of pilgrims and Indians to a new level. We can do more than make neat hats and hand turkeys!

My search of The Gateway to 21st Century Skills for Thanksgiving activities led me to a couple of good resource collections that I want to share with you. The first group of activities is from The Learning Network: Teaching and Learning with the New York Times. These current event based activities extend the topic of Thanksgiving in many unconventional ways. Their lessons are divided into three categories: food and meals, history and culture, and politics and current events. Some lesson topics include the biological effects of overeating, challenges of cranberry farming, American Indian Art, and considering the phenomenon of Black Friday. The site also includes printables, related New York Times articles, and older primary sources for student research.

Scholastic has also put together an extensive compilation of First Thanksgiving activities. Their “Everything for Thanksgiving” site includes lesson plans, interactive web tools, archives of live chats and webcasts, book recommendations, and a virtual field trip to a re-creation of the Plymouth plantation (or Plimoth, as the pilgrims would have spelled it). We tried out the virtual field trip and the virtual tour of the Mayflower. They were both very nicely done. The lesson plans include guides to help teachers use the online tools in classrooms of all different levels.

Using Plimoth Plantation’s “You are the Historian: Investigating the First Thanksgiving” site is like taking your students to an interactive museum exhibit, without all the hassle. The site allows students to view a letter written by a Plymouth colonist, the only eyewitness account of the 1621 harvest celebration, including a translation and a historian’s notes. They can tour a typical colonist’s home and see what daily life was like for members of the Wampanoag tribe. The investigation includes an online tool for students to create their own mini museum exhibit (a printable poster). You might also choose to use this activity as a starting point for a larger investigation. If you do that, you could consider assigning a slide show (try Animoto), a glog, or something we recently discovered: a Museum Box as a culminating project. We found Museum Box in an iLearn Technology blog post. Thanks to Kelly Tenkely for always sharing her finds!

I hope this Thanksgiving season finds your class full of grateful students who are ready to learn all about how the holiday started. Between these collections, Joann’s picks for this week, and our suggestions on Facebook and Twitter, you will be sure to find a Thanksgiving activity that will tie nicely into your plans.

~Peggy's Corner - 11/19/2010~

Transformers

A few weeks ago, my third grader stopped in her tracks, flung her arms far apart, and breathed deeply. Nonplussed, I stopped and asked her what she was doing.

“Remembering the way summer smells,” she said.

I sniffed the air tentatively, but all I could really smell was car exhaust. We were in the middle of a plaza parking lot, after all.

I had forgotten this little scenario until this morning, when we awakened to temperatures in the 40s. As we waited for the school bus, my daughter raised her chin into the wind and announced that it now smelled like fall. “But I still remember how summer smells,” she said.

We live in New England, where summers are fleeting and – for me, anyway – fall arrives much too quickly. The leaves are changing color, pumpkins have appeared on doorsteps, and I can’t seem to keep my hands off a local farm’s seasonal cider donuts. Like spring, autumn seems to be a season when transformations are most noticeable. Plants go dormant, hornet colonies die off, and caterpillars begin constructing chrysalids. The world around us changes continuously via weather, seasons, human-induced development, natural disasters, and so forth. Many examples of transformation are all around us all the time, if we slow down to look.

The concept of metamorphosis has a long and rich tradition. Classic horror stories and legends depict werewolves, vampires, and various types of shapeshifters, all capable of transforming themselves into other guises. Around the year 8 A.D., Ovid published The Metamorphosis, which describes various tales of transformation. Although Ovid’s work is still widely read in academic circles, most people are more familiar with Kafka’s Metamorphosis story of Gregor Samsa, a hardworking salesman who inexplicably awakens one morning as a large insect. While his physical transformation is pronounced, his family too undergoes a metamorphosis in the story, prompting the reader to ask “what is human?”

Metamorphosis is most often demonstrated in the classroom via the lifecycles of various creatures, such as mealworms, butterflies, and frogs. The ability to view these species’ dramatic changes in a relatively short period of time is a fabulous way to illustrate the concept of transformation to students. My picks this week focus on some aspect of metamorphosis, whether it occurs in life science, literature, visual art, or elsewhere. I will be featuring many more resources for all ages throughout the week on our Facebook and Twitter pages, so please be sure to check in to view them.

The Metamorphosis by Franz Kafka
Subjects: Literature, Writing
Grade: 9-10
In this lesson, students analyze the many interrelated literary elements and universal themes in Kafka’s seminal short story. Students are asked to delve much deeper into the story’s symbolism beyond Gregor’s literal transformation into a bug as they examine the effects of society, family, stress, and environment on the characters. This lesson is offered by LEARN NC, a program of UNC Chapel Hill School of Education that provides lesson plans, professional development, and other resources to support teachers. The lesson is aligned to North Carolina state standards.

Claymation Metamorphosis
Subjects: Art, Life science
Grade: 5-12
Like Gumby, but educational! This lesson provides an introduction to the basics of Claymation and media production using a familiar scientific theme — the metamorphosis of a butterfly. This lesson is produced by Blick Art Materials, an art supply company that also offers lesson plans and video workshops for teachers. The lesson is aligned to national standards.

How a Caterpillar Becomes a Butterfly
Subjects: Life science
Grade: K-1
This activity introduces young students to the life cycle of a butterfly. Students role play and draw the various stages that a caterpillar goes through to become a butterfly. Students also listen to and discuss Eric Carle’s classic book The Very Hungry Caterpillar. This lesson is offered by the Educators Reference Desk, a repository of lesson plans, resource guides, and AskERIC Q&A archives from the Information Institute of Syracuse at Syracuse University.

~Joann's Picks - 10/7/2010~