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Caught Reading: Measuring Penny

Engaging students in measuring objects and space around us is active and fun! Remember, measuring is always doing – and we all measure, all the time. Consider how often you hear questions that start like this:

Lauradaughterreading

My daughter and I recently got caught reading Measuring Penny. While reading, we talked about how we measure qualities of the world every day, including length, volume, and time.

How much…

When will it be time to…

How big…

Will this fit…

Do I have enough…

How old…

Is this too much…

How do these compare…

We ask these kinds of questions every day at home, at school, at work, at the store, on the bus, and at the park. Be sure to tell your students how answering these kinds of questions involves mathematical thinking and increases our reasoning and analytical skills. Use examples and point out the connections between investigation, measurement, and number.

While measurement is often viewed as a matter of procedure, there’s really more to it. Think about what features of certain objects and spaces are measurable, and why we even care about size and scale. Think about comparisons. Think about magnitude. Think about precision and estimation; whole units and parts. All of these ideas are fundamentally related to measurement, and contribute in important ways to our awareness of and actions in the world.

Determining the amount, size, or degree of something is necessary and useful. This is clearly illustrated in Loreen Leedy’s Measuring Penny. In this story, Lisa learns a lot about her dog, Penny, by measuring. Lisa measures Penny’s height, compares Penny’s weight to other dogs’ weight, considers how much food and water Penny needs every day, and calculates how fast Penny runs. Lisa is identifying many different measurable attributes of Penny and being her care-taker. She uses different tools and both standard and non-standard units to measure and explore. She is deepening her understanding of quantities and number and enriching her perspectives on her special pal, Penny, and what it means to take care of a pet. Illustrations in the book show us how to measure and why measuring can be so powerful!

Consider using books like this in your classroom. Be sure to highlight these big ideas related to measurement that help us bring conceptual understanding and procedural understanding together.

Big Idea #1: Identifying, describing, and comparing measurable attributes of objects around us helps us make sense of everyday life.

Big Idea #2: Specific techniques, tools, and formulas are used to determine measurements.

Measure and explore with your students, and share your thoughts and reactions in the comment section below. Tell us how you develop understanding of measurement in your work with children.

For additional ideas and materials on this topic, check out

Annenberg Learner’s Learning Math: Measurement for K-8 teachers

Eames Powers of Ten

Literacy in the 21st Century

Written by WGBH Education for Annenberg Learner, Part 2 of 3 (Go to Part 1)

LIT 16“Literacy is no longer a static construct from the standpoint of its defining technology for the past 500 years; it has now come to mean a rapid and continuous process of change in the ways in which we read, write, view, listen, compose, and communicate information.” (Coiro, Knobel, Lankshear, & Leu, 2014. Handbook of research on new literacies.)

Traditional views of literacy learning and development are changing to reflect a more global view of understanding and communicating in today’s increasingly complex world. It will come as no surprise that students spend a lot of time using technology outside of school. But what teachers are beginning to think more about is how this explosion of technology impacts the ways students read, write, think, and communicate about their world. Whether engaged in social media, texting, making videos, sharing images, reading e-books, or navigating the Internet, students are using a variety of literacy practices and tools. Combining these practices with other outside-of-school activities in which literacy plays a part—such as independent reading, writing, performance, and even sport—it becomes evident that many students engage in substantial literacy-based activities beyond their schoolwork. There is a high degree of motivation when students select their literacy practices and venues. Given this, it is important for teachers to understand the out-of-school literacy practices students bring to school and to relate them to school-based learning. This connection will expand and enhance their use of multiple literacies.

“Students engage in literacy practices and learning outside of school, learning they consider powerful and important. Typical approaches to secondary school content learning often overlook the learning and literacy practices that youth engage in apart from their school-based, content learning (Moje, 2008).”

Given the knowledge and expertise students have in using technology outside of school, digital literacy can play a significant role in school as a way to maximize productive learning. This requires instruction in new literacies, including how to determine where to find relevant information, analyze and evaluate websites, summarize and synthesize important information, incorporate videos, music, and other media of students’ choice into performance assessments, and produce projects that illustrate understanding. For example, when students are taught to evaluate the authenticity and reliability of websites, they are using the social studies strategies of sourcing and contextualization. When students create or locate images, or incorporate music into a project, they are making connections and demonstrating their interpretation and synthesis of key ideas. When done effectively, technology can provide a critical connection between home and school literacy and change the often-held view by students that reading and writing are things you only “do” in school.

For examples of how to blend these practices, check out the following:

Lapp, Fisher, Frey and Gonzalez (2014). Journal of Adolescent & Adult Literacy 58(3) November 2014 doi: 10.1002/jaal.353 © 2014 International Reading Association (pp. 182–188).

Lapp, Thayre, Wolsey, Fisher, 2014. June 2014 doi:10.1598/e-ssentials.8056 © 2014 International Reading Association.

Are you ready to incorporate discipline literacy strategies into your curriculum? Learn how with Reading and Writing in the Disciplines.

Read part 1 of this blog series on discipline literacy: “How Does Discipline Literacy Differ from Content-area Literacy?

How Does Discipline Literacy Differ from Content-area Literacy? – See more at: http://learnerlog.org/socialstudies/how-does-discipline-literacy-differ-from-content-area-literacy/?preview=true&preview_id=3168&preview_nonce=8d8bf65a26#sthash.6JEXI13f.dpuf
How Does Discipline Literacy Differ from Content-area Literacy? – See more at: http://learnerlog.org/socialstudies/how-does-discipline-literacy-differ-from-content-area-literacy/?preview=true&preview_id=3168&preview_nonce=8d8bf65a26#sthash.6JEXI13f.dpuf

How Does Discipline Literacy Differ from Content-area Literacy?

Written by WGBH Education for Annenberg Learner, Part 1 of 3 (Go to Part 2)

LIT 15

Reading and Writing in the Disciplines

When students enter middle and high school, their teachers expect them to have mastered the basic skills and strategies necessary for reading and comprehending texts across disciplines and genres. Is this always the reality? Do the skills and strategies they’ve developed serve them equally well when they read a scientific journal article, mathematical proof, historical primary source document, Shakespearean sonnet, and technical paper?

The answer is, no. While basic strategies such as making connections, asking questions, inferring, summarizing, and monitoring understanding are important when reading across subjects, they are not sufficient unless they can be adapted to each discipline. Even if students have mastered these basic skills, they may still struggle to understand, analyze, interpret, and evaluate important ideas in discipline-specific texts because they do not have the topical language and specialized reading practices that are used by scientists, mathematicians, historians, literary analysts, and technical specialists. To understand how each discipline produces and communicates key ideas, students need to know what is specifically involved when reading across these disciplines. So how exactly is this discipline literacy different from content-area literacy?

Content-area Literacy

Content-area literacy strategies are traditionally defined as the basic set of strategies students use when reading and responding to texts, with little differentiation being made across the content-area subjects. For example, students may learn techniques for determining important information, making inferences, asking questions, and summarizing. They would then apply these strategies when reading science, history, and math.

Discipline Literacy

Discipline literacy skills support students in moving beyond the general reading strategies as they develop specialized practices for making sense of discipline-based texts through reading, writing, and oral language. These practices include understanding how information is presented in each discipline: organization of important information; specialized vocabulary and syntactic nuances; use of text features; and interpretation and evaluation of evidence. The focus is on teaching students different ways of thinking as they encounter texts by developing reader identities within each discipline—to become expert readers and communicators in a discipline by reading, writing, and talking like a historian, a scientist, a mathematician, etc.

Essentially, “[t]he difference is that content literacy emphasizes techniques that a novice might use to make sense of a discipline text (such as how to study a history book for an examination) while discipline literacy emphasizes the unique tools that the experts in a discipline use to engage in the work of that discipline” (Shanahan and Shanahan, 2012, p. 8).

What Does This Mean for Instruction?

It has been an unspoken expectation that elementary teachers would help students have content-area literacy skills in place by middle school. In contrast, the expectation around discipline literacy is that it’s the job of discipline teachers to build these skills. But in reality, these are not isolated tasks.

The Common Core State Standards have placed an emphasis on the need for ELA and discipline teachers to share the responsibility for teaching and assessing mastery of the ELA Standards. While this call for shared responsibility is certainly a change from what has occurred in schools for decades, it’s important because it has now been documented that discipline experts approach the reading of texts differently (Shanahan and Shanahan, 2008).

This does not mean that discipline teachers must also add “reading teacher” to the many hats they already wear. Rather, it means that they should model and share their own strategies for how to approach a text, how to determine and synthesize key ideas, how to critically evaluate the content, and how to engineer new possibilities. After all, who else is better able to support the reading of texts within a discipline than a discipline expert who knows the language and understands how students acquire text-based information?

They are, after all, the experts.

Shanahan, T., & Shanahan, C. (2008). Teaching disciplinary literacy to adolescents: Rethinking content-area literacy. Harvard Educational Review, 78(1), 40–59.

Are you ready to incorporate discipline literacy strategies into your curriculum? Learn how with Reading and Writing in the Disciplines.

Read part 2 of this blog series on discipline literacy: “Literacy in the 21st Century

Are you ready to incorporate discipline literacy strategies into your curriculum? Learn how with Reading and Writing in the Disciplines. – See more at: http://learnerlog.org/socialstudies/how-does-discipline-literacy-differ-from-content-area-literacy/?preview=true&preview_id=3168&preview_nonce=8bf5a75fad#sthash.YEQZS0jD.dpuf
Read part 1 of this blog series on discipline literacy: “How Does Discipline Literacy Differ from Content-area Literacy?” – See more at: http://learnerlog.org/socialstudies/literacy-in-the-21st-century/#sthash.aM3Bw6Qw.dpuf
Read part 1 of this blog series on discipline literacy: “How Does Discipline Literacy Differ from Content-area Literacy?” – See more at: http://learnerlog.org/socialstudies/literacy-in-the-21st-century/#sthash.aM3Bw6Qw.dpuf

More Than Just Numbers: Math Awareness Month

AAO_3_Lightning4Have you ever listened to weather forecasts and wondered whether there’s any difference between partly cloudy and mostly cloudy, or a chance of rain versus a slight chance of rain? In fact, all of those terms have precise meanings based on probabilities. If the sky is partly cloudy, about three to four eighths of it will be covered by clouds, and a slight chance of rain means the odds are about 20 percent that at least 0.01 inches of rain will fall somewhere in the forecast area.

Weather forecasts illustrate the central role that math plays in many aspects of everyday life. They are based on sophisticated computer models that analyze data from weather balloons, radar, and satellites. Modern weather forecasting saves lives and money by warning us in advance of major storms.

Mathematics organizations have designated April as Mathematics Awareness Month. This year’s theme, “Math Drives Careers,” focuses on the many fields where math plays an important role, from energy production to medicine to business. Many of these jobs don’t have “mathematician” in the title, but draw heavily on math and statistical skills.

Consider some of the ways in which math shapes your day beyond providing a weather forecast. Transit companies use algorithms to map the most efficient routes and schedules for the buses we ride to work and school. Utilities use math to forecast how much power they will need to keep our air conditioners running on hot days. Grocery stores use formulas to track how well goods are selling and decide when to mark down prices. And statisticians quantify how well our favorite sports teams are doing.

Spotlight math from many angles with the following resources:

Use Learning Math: Measurement to discuss the importance of measurements with elementary and middle school students. How do we rely on accurate measurements of weight, volume, and distance in our daily lives?

Against All Odds: Inside Statistics shows high school students how concepts like probability and inference can be used to understand topics such as weather, the spread of disease, and impacts of pollution in the environment.

For advanced students, Mathematics Illuminated explains uses for more complex concepts, such as infinity, game theory, and networks.

Many science courses on Learner.org also cover topics that are based on math. For example, unit 6 of Chemistry: Challenges and Solutions, “Quantifying Chemical Reactions,” explains why summarizing chemical reactions accurately and understanding the ratios in which elements combine are critical to producing chemicals efficiently and avoiding waste.

Unit 6 of The Habitable Planet, “Risk, Exposure and Health,” discusses how scientists quantify risks from exposure to different kinds of hazards in the environment and identify causal relationships between exposure and health impacts.

What are the odds that you can show your students how math shapes their lives?

Eadweard Muybridge: Photography and Film Pioneer

English expatriate Eadweard Muybridge (April 9, 1830-May 8, 1904) is one of the most influential people in the history of American film. He was a pioneer in film and artistic photography, as well as in scientific and industrial photography. His exciting work has connections to art, social studies, science, and mathematics topics.

PUPMath_Kid looking at Muybridge work

A student looks at Eadweard Muybridge’s photographic study of animal motion. From Private Universe Project in Mathematics.

Art: Muybridge took daring steps, cutting down trees and venturing into dangerous places, to get landscape photographs that would distinguish him from his contemporaries. See the story of his shot, Falls of the Yosemite, taken in 1872 while on a six-month trip West in Art Through Time, program 10, “The Natural World.”

Social Studies: Find a slideshow of 17 of Eadweard Muybridge’s images of Guatemala in Teaching Geography, workshop 2, “Latin America.” Below each slide is information about the content of each photo and questions to compare the past with the present.

Science and film: Muybridge developed photography techniques that captured human and animal movements in new ways. Read about these techniques in American Passages, unit 8, “Regional Realism.”  Muybridge also invented the zoopraxiscope (image #8245 in the archives), a device that projected a moving image from still sequences.

Math: In the video for workshop 6, “Possibilities of Real Life Problems,” of Private Universe Project in Mathematics, ninth graders are asked to solve how fast a cat, captured in a series of photos by Eadweard Muybridge more than 100 years ago, was moving in frames 10 and 20.

Teach Students to Like Math

Teaching Math Library, K-4, program 6, "Animals in Yellowstone" Fourth- and fifth-graders develop number sense and meaning for large numbers by estimating how many bison, elk, and pronghorn they saw on a field trip to Yellowstone National Park.

Teaching Math Library, K-4, program 6, “Animals in Yellowstone”
Fourth- and fifth-graders develop number sense and meaning for large numbers by estimating how many bison, elk, and pronghorn they saw on a field trip to Yellowstone National Park.

No Math = No Fun

Know Math = Know Fun!

Math has a special kind of beauty and appeal to the person who is willing to look. Yet we know there are students who don’t know how to look, and there are students who look and are unable to see. There are also students who don’t want to look because they think they don’t like math or won’t “be good at it.” It can certainly be hard to help all students see math as interesting and approachable, but if we can shift our students’ perspectives, we can make a big difference.

Before you design ways to motivate and inspire your students to like and do math, you have to consider your own perspective on mathematics. What does mathematics mean to you? What appeals to you about mathematics? When is doing math fun for you?

To me, math is patterns, puzzles, and polygons. It’s the path of a ping-pong ball and the structure of a palace. Math is a model of the moon that we can study. Math is really big and really small. It’s interconnected. It’s practical. It’s fun. The power of math is seen in objects around us, processes, and predictions. Without math we wouldn’t have efficiency, production, and invention.

Ask your students, What does mathematics mean to you? What appeals to you about math? When is doing math fun for you? What they say and how they say it brings awareness, and from there you can take action.

Here are several steps you can take to promote new and different ways for your students to see math and to have fun doing math. Let’s get all kids to look at math with interest and enthusiasm!

1: Promote curiosity about how the world works.

Start a list of students’ curiosities. Record questions, confusions, and criticisms. Ask and explore real world situations: What math is relevant here? How might some aspect of mathematics help us understand and describe this situation? Can math help us determine ways to change or improve this situation?

2: Ask students to stop and really look at ordinary objects and events around them.

Take time to notice details. Look for structure. What are the parts of that ordinary object? Look for patterns, relationships, and magnitude. What grows? What shrinks? What repeats? How is this connected to that? What features of objects are measurable? Mathematical ideas are revealed when we look more and see more.

3: Tell your students the story of mathematics. Think characters, setting, plot.

Help students make sense of the origins and evolution of mathematical ideas. Who wanted to know what? Why? Who did what? What happened as a result? The interaction between mathematical thinking and human activity is incredible! Push students to make connections between the past and the present. Use the story of mathematics to help them think about the future.

I have used the ideas above in my own classrooms with students in kindergarten and students in college. I think they’re powerful and exciting. They increased engagement and productivity in my classroom, and led to some of the most interesting learning experiences I ever had as a teacher.

If these ideas are interesting to you, have fun and try them out! Ask those questions. Explore and learn with your students, and share your thoughts and reactions in the comment section below.

The main idea in this blog is inspired by the work and writing of Harold R. Jacobs. For more information, check out his book, Mathematics: A Human Endeavor.
Some other ideas in this blog are inspired by the work and writing of G. Polya. For more information, check out his book, How to Solve It: A New Aspect of  Mathematical Method.

For additional ideas and materials on this topic, check out

Mathematics: What’s the Big Idea? This video workshop offers motivation and tools for K-8 teachers who want to explore ways of changing how they teach math.
Teaching Math Libraries, K-4, 5-8, and 9-12 These video programs demonstrate how teachers guide and assess student understanding, and offer strategies for keeping students motivated and engaged.

Selfie: Bringing Personal Meaning to Photos

EssentialLens_MakedaBestWhen students see a photograph in a classroom, a textbook, or a school project, they often treat it just like a poem or short story: they try to clearly state what the photo “means.” They believe that a photo has a unique, incontestable meaning that is clear to the perceptive viewer. A photographer wouldn’t take a photo without having a message in mind, the reasoning goes, so that message must be clear in the photo s/he took, and if I can’t find it, there’s something wrong with me.

It’s hard to convince students that this is not true (for photos or for poems and short stories, but we’ll stick with photos here). Photos cross a line between art and reportage. They can have a clear message when they are reportage. When they are art, they are open to almost endless personal interpretation. When they are a mix of both, photos can challenge the most perceptive viewer. The student looking at the photo is not just a data analysis machine taking in information and processing it. The power of photos is in their immediacy: they are shots of real people in real situations that the viewer takes in through the lens of her or his own life experience. In short, the viewer makes the meaning. As historian of photography Makeda Best puts it, instead of stopping at asking ourselves and our students what we see in a photo, we have to “look more closely and ask questions of why we see what we see.” This is a big shift. It gives the student authority over the photo instead of the other way around.

To teach students to use their own experiences to analyze a photo, practice on the photo mentioned below using the Focus In activity from Essential Lens: Analyzing Photographs Across the Curriculum. (Watch Makeda Best demonstrate the Focus In activity in the “A Closer Look” video.):

Start with Dorothea Lange’s masterpiece “Migrant Mother,” taken in 1936. Students may have seen it before. It is one of the most famous photos in the world. Too often, students move past their initial emotional reaction to this photo to try to discern its objective meaning. Following the steps in the Focus In Method for Analyzing Photographs, try to get your students back inside their own heads and hearts and experiences as they analyze “Migrant Mother.” Click on the link for a detailed description of each Focus In step. This step-by-step process can take the burden of finding meaning off students by encouraging them to make meaning.

Focus In Steps

Step 1: Observe

Step 2: Build on Your Observations

Step 3: Make Inferences

Step 4: Formulate Further Questions

Note: Here is a link to information about the photograph “Migrant Mother.”

 

How are you using photographs in your classes? Share in the comment section below.

Learning from the 2014 Nobel Prizes

Perhaps the Nobel Prizes recipients don’t make the same headlines as baseball’s World Series challengers, but every October the stories behind their work are just as exciting. These are discoveries, theories, works of art, and acts of humanity that have been years in the making. The work touches us in fundamental ways and constitutes the “shoulders of giants” referred to by Isaac Newton. If you don’t quite understand the laureates’ achievements, you can see the fundamental principles and related concepts at learner.org.

MathIllum_rockpaperscissors

Learn how game theory applies to “rock, paper, scissors” in Mathematics Illuminated.

Sveriges Riksbank Prize in Economics

Jean Tirole, a French theoretical economist, won the award for analysis of market power and regulation. Tirole studied how to regulate industries with a few powerful firms, such as telecommunications firms. You can hear from Nobel committee chair Tore Ellingsen on the significance of Tirole’s work.

Tirole’s work was based on the mathematical concepts of game theory, which you can learn about in Mathematics Illuminated, unit 9.  The online text provides familiar examples, including zero sum games, and prisoner’s dilemma. Watch the video to see how game theory even applies to “rock, paper, scissors.”

Once you have a handle on game theory, see how government regulations have been applied to big players in the auto, energy, and airlines industries in Economics U$A, program 7, “Oligopolies.” This program looks at how big industries manage to write the rules of the marketplace.

Nobel Prize in Medicine or Physiology and Nobel Prize in Chemistry

Several of this year’s laureates followed the principle of thinking small. The medicine/physiology and chemistry prizes involve looking at objects down to the size of a single cell or molecule. The Nobel Prize for Medicine or Physiology was awarded to three researchers who found the brain’s mechanism for establishing our position in space, a mental GPS-like system. John O’Keefe found that we carry “space cells” in our brains and May-Britt Moser and Edvard I. Moser expanded the concept to a grid in which these cells operate.  The Nobel Prize in Chemistry was awarded for work in microscopy allowing scientists to see down to this level at “super resolution.”

This level of microscopy has applications across all fields of science research. Wolfhard Almers at the Vollum Institute in Portland, OR explains how, using wave microscopy, he and his colleagues were able to isolate a single nerve cell to understand what it does after releasing a transmitter. His research is covered in Rediscovering Biology unit on Neurobiology.

“I still haven’t gotten over thinking it’s really cool, that I can go into work every day and take pictures of atoms and I can see individual atoms with this microscope,” says graduate student Tess Williams. The lab where she works at Harvard investigates the structure of superconducting materials. Find out more in Physics for the 21st Century unit “Macroscopic Quantum Mechanics.”

Nobel Prize in Physics

The three physicists who shared the Nobel Prize in physics gave new meaning to “keeping the lights on.” They invented a new energy-efficient and environment-friendly light source – the blue light-emitting diode (LED). In the LED, electricity is directly converted into light particles, photons, leading to efficiency gains compared to other light sources where most of the electricity is converted to heat and only a small amount into light. Explore the many facets of light and heat with your students in the workshop series Shedding Light on Science, especially unit 2, “Laws of Light.

Nobel Peace Prize

Indian and Pakistani activists Kailash Satyarthi and Malala Yousafzai attracted the attention of the international community to the issue of child rights and shared the Nobel Peace Prize. From the earliest waves of immigration in the U.S., children have been used as workers and denied a formal education. Thomas Rivera wrote about his experience as a migrant child agricultural laborer in the memoir, “And the Earth Did Not Devour Him/Y la Tierra no se traiga.” Read about Rivera’s background in American Passages, unit 12, “Migrant Struggle.” His translator, Evangelina Vigil-Piñón discusses Rivera’s work and its place in Chicano literature in the Learner Express: Language Arts modules.

Inspiring Women in Mathematics

Courtesy: Maryam Mirzakhani Professor Maryam Mirzakhani is the recipient of the 2014 Fields Medal, the top honor in mathematics. She is the first woman in the prize’s 80-year history to earn the distinction. The Fields Medal is awarded every four years on the occasion of the International Congress of Mathematicians to recognize outstanding mathematical achievement for existing work and for the promise of future achievement.

Photo Courtesy: Maryam Mirzakhani, Professor Maryam Mirzakhani is the recipient of the 2014 Fields Medal, the top honor in mathematics. She is the first woman in the prize’s 80-year history to earn the distinction.

Maryam Mirzakhani of Stanford University made history earlier this month, becoming the first woman to win the Fields Medal in the 78-year history of the award. The honor, bestowed every four years to two to four mathematics researchers under the age of 40, is often thought of as the Nobel Prize for math.

According to the International Mathematical Union, the 37-year-old, Iranian-born Mirzakhani won “for her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces.”

Mirzakhani realizes that her unprecedented achievement transcends mathematics research. “This is a great honor. I will be happy if it encourages young female scientists and mathematicians,” Mirzakhani, quoted by Stanford News, said. “I am sure there will be many more women winning this kind of award in coming years.”

Even though, according to a 2013 National Science Foundation report, female students take precalculus/analysis and algebra II at higher rates than male students during their K-12 education, they lose that ground during their undergraduate education, earning only 43.1 percent of all bachelor’s degrees in mathematics and statistics. These disparities become even greater when students’ racial and socioeconomic statuses are taken into account.

Mirzakhani’s accomplishment is good news for educators, providing them with an example of a mathematics trailblazer to inspire students from underrepresented groups. While she is the latest to break through a long-preserved mathematics glass ceiling, Mirzakhani certainly is not the first.

Nergis Mavalvala

Nergis Mavalvala

One of the women benefitting from Mirzakhani’s work is MacArthur Prize winner and physicist Dr. Nergis Mavalvala of MIT. She and her team design experiments to detect ripples in the fabric of space-time known as gravitational waves. See her in Physics for the 21st Century, “Gravity.”

Sophie Germain

Sophie Germain

Sophie Germain (1776-1831) didn’t let the École Polytechnique’s policy against admitting women stop her from pursuing an education. Though she began her educational career submitting papers under the false name Monsieur Antoine-August Le Blanc, Germain gained the esteem and mentorship of prominent mathematicians and became well known for her work in elasticity theory and number theory. In number theory, a prime number (p) is a Sophie Germain prime if 2p + 1 is also prime. Explore the basics of prime numbers and number theory in Learning Math, session 6, “Number Theory.”

While the name Albert Einstein is synonymous with mathematical genius, fewer people have heard of Emmy Noether, a mathematician whom Einstein himself once called “the most significant creative mathematical genius thus far produced since the higher education of women began.”

Emmy Noether

Emmy Noether

Like many historic female mathematicians, Noether encountered unjust obstacles throughout her distinguished career. The University of Erlangen in Bavaria, Germany prevented her from fully participating in classes, allowing her to audit them instead. Despite her brilliance and the respect she garnered from her contemporaries, Noether spent years teaching without pay.

While Noether was widely recognized for her accomplishments by the early 1930s, in 1933 Germany’s Nazi government forced all Jews out of all government positions. Noether fled Germany for the safety of the United States and a position at Bryn Mawr College in Pennsylvania, though she died just two years later at the age of 53.

Mathematics Illuminated, unit 6, “The Beauty of Symmetry,” discusses Noether’s eponymous theorem as well as her contributions to algebra and physics.

Dorothy Wallace, a content advisor for Mathematics Illuminated (units 6 and 10) and professor at Dartmouth College, is an accomplished mathematician and educator. Dr. Wallace contributed to the Mathematics Across the Curriculum project. Funded by a grant from the National Science Foundation, MATC aims to integrate math throughout the undergraduate curriculum using interdisciplinary courses and materials. Her writing and editing credits include Numeracy!, the ejournal of the National Numeracy Network and The Bell that Rings Light (World Scientific Press).

Another branch of mathematics, statistics, is used by computational geneticist Dr. Pardis Sabeti at Harvard. She has developed algorithms to detect the genetic signatures of adaptation in humans and microbial organisms. Learn about her work with West Africans who are vulnerable to deadly Lassa fever in Against All Odds: Inside Statistics, “Inference for Two-Way Tables.”

Pardis Sabeti

Pardis Sabeti

From the ancient Greek philosopher Hypatia to Mirzakhani, there are many historical and contemporary examples of women in mathematics to encourage female students interested in pursuing a career in the field.

Add to this list in the comments below.

Get Ready: Build a Learning Community

Get ready, get set! But before you go, step back and consider the bigger picture. What will your classroom look and feel like? How will students interact with each other? How will they express themselves and share ideas? Teach your students to be learners together and to respect differences by developing a sense of community. See the following examples for different grade levels and subject areas:

Social<br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />
                                                          Studies<br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />
                                                          Library1. Teach students how to discuss and appreciate differences within their classroom community. For example, in Social Studies in Action: A Teaching Practices Library, K-12, program 31, “Dealing with Controversial Issues,” students learn how to conduct informed and open discussions that include multiple perspectives about gender-based discrimination, conflict in the Middle East, and other issues.  Program 30, “Unity and Diversity,” deals with teaching students to appreciate the different cultures of their community.

2. Plan your writing community before the year starts. Take a look at Developing Writers: A Workshop for High School Teachers, workshop 1, “First Steps.” Think about how much time students will spend writing, getting and giving feedback from peers, and reviewing their own work. In workshop 2, “A Shared Path,” you’ll consider the characteristics of a writing community and learn to set up effective writers’ groups.

3. Build a safe middle school writing environment from the beginning of the year. In Write in the Middle: A Workshop for Middle School Teachers, workshop 1, “Creating a Community of Writers,” see teachers model participation in a writing community.

4. Involve parents and guardians. Watch how a teacher extends a 3rd grade book community using activities and discussions that involve the students’ parents, grandparents, and friends in Teaching Reading 3-5 Workshop, classroom program 10, “Fostering Book Discussions.” Students also learn how to generate discussions in small groups.

5. Set up classroom routines that help young students become positive, more self-directed learners using strategies from Teaching Reading K-2 Workshop, workshop 1, “Creating a Literate Community.”

6. Foster effective communication and mathematical thinking with strategies provided in Teaching Math Grades K-2, session 2, “Communication.” Help young students express their understanding of math concepts through oral, written, and visual (symbols, pictures, gestures) communication.

What are ways you build a learning community in your classrooms?