Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Search
MENU

Inspiring Women in Mathematics

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.

Teaching Math girl at chalkboard

A student explains a problem to the class. From Teaching Math Library, 9-12.

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?

Observe and Learn from Effective Teachers

Teachers take the stage every day in front of their students, striving to instruct, engage and guide. Being observed by a classroom of students is the norm. As Matthew O. Richardson points out in his journal article [1] for the National Education Association, “Teachers stand before others and put on a personal exhibition every time they lecture, lead a discussion, or guide a role-play.” Why is it, then, that the prospect of peer observation is potentially unnerving to many teachers?

TeachingMath_6

From Teaching Math, 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.

While discussing the growing trend of peer-to-peer learning for teachers, Education World acknowledges that the practice of peer observation (which is becoming more widely discussed in both university, and secondary and elementary environments) is meant to be a collaborative form of professional development, not an evaluation tool. Education World notes that learning by observing can reap benefits for teachers, administrators, and schools. They quote Dr. William Roberson, who served as co-director of the Center of Effective Teaching and Learning at the University of Texas-El Paso, as making this bold statement:

Easily, peer observation is more valuable than other forms of professional development, if the proper context is created. If done well, it is carried out in a real, practical, immediately relevant situation. Compare that to attending workshops or conferences in which participants remain at a certain level of abstraction from their own classrooms.

Ideally, peer-to-peer learning allows the observing teacher to reflect on their own practices and methodology in, as Roberson puts it, an “immediately relevant situation.”

Are you thinking about working peer observations into your schedule next year? Here are some resources for observing teachers in your own school and for observing teachers at your convenience.

Using checklists to focus your observations on specific goals:

Using checklists is a great way to get the most out of your observation experiences. Start by having a goal in mind. For example, is your goal to improve classroom management, track student achievement, or create more engaging lesson plans? Then, focus your observation on ways to meet that goal. Checklists are useful for narrowing your focus.

Look at some examples of teacher observation checklists below. Even if the examples are not in your subject area or grade level, you can glean ideas for developing your own checklists.

  1. This observational checklist from Teaching Reading, Grades K-2 allows a fairly straightforward evaluation of a peer teacher’s methods of developing the essential elements of literacy. Observing teachers have space to comment on their colleagues use of shared and independent reading and writing, among other practices.
  2. The Literacy Development Chart, also from Teaching Reading, Grades K-2, allows ongoing observation of a peer teacher to see how an individual student “case study” develops and how a teacher supports their progress based on the student’s strengths and needs.
  3. The Key Questions observation form provides a more open-ended way for teachers to observe their colleagues. This example asks questions related to how students develop literacy skills. The form’s prompts include questions on how reading and writing are connected and how a peer teacher instructs students with diverse needs.
  4. Searching “classroom observation checklist for teachers” on Google yields many very useful checklist formats.

Videos for observing expert educators on your own schedule:

Finding time during the school day for such detailed peer observation is not always feasible. In addition, a teacher who wants to use observation as a means to improve their own practice may encounter other obstacles; a culture of trust and a willingness to participate has to be present in their school already. Don’t have opportunities to observe peers at your school? Learner.org provides video examples of effective teaching in most subject areas and most grade levels.

The Learner.org workshops in the list below can be streamed for free. Here are just a few highlights:

  1. Teaching Reading, Grades K-2 could be used in conjunction with the aforementioned observation forms as an alternative to watching live classrooms. The extensive video library includes 30 minute programs on classroom practices in action as well as student case studies of children in grades K-2.
  2. In The Art of Teaching the Arts, workshop 3, “Addressing the Diverse Needs of Students,” watch how three teachers adjust their teaching approaches for students with various learning styles and needs.
  3. Making Civics Real, a professional development workshop for high school teachers, illustrates an activist approach to the teaching of civics. For example, in workshop 6, “Civic Engagement,” observe a Human Geography class taught by Bill Mittlefehldt. Students work in teams on a service project to solve community issue.

Here are more resources showing effective classroom instruction that can be used for observations:

The Arts:
The Arts in Every Classroom: A Workshop for Elementary School Teachers
Connecting With the Arts: A Workshop for Middle Grades Teachers
The Art of Teaching the Arts: A Workshop for High School Teachers

Foreign Languages:
Teaching Foreign Languages, K-12 Library

Language Arts and Literature:
Teaching Reading, K-2
Inside Writing Communities, Grades 3-5
Making Meaning in Literature, Grades 3-8
Teaching Multicultural Literature: A Workshop for Middle Grades
Developing Writers: A Workshop for High School Teachers
The Expanding Canon: Teaching Multicultural Literature in High School

Mathematics:
Teaching Math: A video library, K-4
Teaching Math: A video library, 5-8
Teaching Math: A video library, 9-12
Insights into Algebra I: Teaching for Learning (middle and high school)

Social Studies:
Social Studies in Action: A Teaching Practices, Library K-12
The Economics Classroom: A Workshop for Grade 9-12 Teachers
Making Civics Real: A Workshop for Teachers (high school)

Science:
Science K-6: Investigating Classrooms
Teaching High School Science

While the best way to learn from expert teachers is to watch them in person, watching examples of excellent teaching in videos can be just as useful. In addition, you can observe these classrooms at your convenience and pause and re-watch sections as needed.

We are interested: Share your experiences using classroom observations to improve your instruction below the post.

[1] Richardson, Matthew O. “Peer Observation: Learning From One Another,” The NEA Higher Education Journal 16. No. 1 (2000): 9-20.

 

How to Share Ideas From Your Classroom

sharing ideasWe know you create amazing lesson plans and activities using Learner.org resources. Share them with other teachers on the Ideas From Your Classrooms section of our blog.

Submit your lesson plans and activities to blog@learner.org for consideration. We will post a new activity or lesson plan every Tuesday. Check back often to learn about fresh ideas from your peers.

Also, in the Ideas From Your Classrooms section of the blog, we encourage you to comment under lesson plan and activities posts, respond to questions about your classrooms, and support each other with knowledge and advice from your teaching experience.

 

How to Submit a Lesson Plan or Activity

Your plans and activities should state a clear objective, be well-organized, require minimal to no edits, and incorporate a Learner.org resource. (You may also refer to additional resources if desired.) The Learner.org resource you refer to can be a whole series, or part of a series such as an online textbook chapter or video program, an online interactive, or any other resources accessed free on our website. Series titles and urls must be included.

We look forward to hearing from you!

Please include the following information with your materials:

  1. Your name and email address
  2. Title of the activity or lesson plan
  3. Subject/ Class name
  4. Grade level
  5. School name or location (not required)

Also, please share this post! Thank you. Don’t forget to subscribe to LearnerLog.org so you don’t miss new postings.

9 Ways to Encourage Play for Kindergarten Day and Every Day!

ArtsEvery_11Time to pull out the blocks and finger paints. Kindergarten Day recognizes the importance of play, games, and creative activity in children’s education. In 1837, Friedrich Froebel, born April 21, 1782, established the first kindergarten in Germany. German immigrants brought the idea to the U.S. in the 1840s. In 1873, the first public kindergarten was started in St. Louis, MO.

Kindergarten classrooms of the past provided oodles of time for students to use their imaginations, develop social skills, and learn to love learning. As the arm of standardized testing reaches into the earliest years of childhood development, concerns are raised about the disappearance of play experiences. Read about why playtime is important for young students in this report from the Alliance for Childhood.

Meanwhile, in the spirit of Friedrich Froebel, we present the following ideas for using play to teach literacy and math skills, as well as concepts for social studies and science:

1. Students learn to appreciate different cultural backgrounds as they explore holidays such as the Chinese New Year and Valentine’s Day in Teaching Reading K-2 Library, program 3, “Building Oral Language.” Sensory activities and crafts are combined with reading and writing activities to help students make connections.

2. Chuck Walker pairs kindergartners with 6th graders for counting activities located inside and outside of the classroom in Teaching Math, A Video Library, K-4, program 3, “Math Buddies.”

3. Students learn about story structure and engage their imaginations when theatre artist Birgitta De Pree visits the classroom in The Arts in Every Classroom: A Video Library, K-5, program 10, “Bringing Artists to Your Community.”

4. Thalia’s teachers tap into her interests and add whimsy with song and drawing to literacy lessons for this energetic kindergartner in Teaching Reading K-2 Library, program 4, “Thalia Learns the Details.”

5. Young students learn mathematical concepts while playing with different types of manipulatives in Teaching Math, A Video Library, K-4, program 7, “Cubes and Containers,” program 12, “Dino Math,” and program 43, “Beans, Beans, Beans.”

6. Students understand economic concepts of supply and demand while working together to make bread in Social Studies in Action, A Teaching Practices Library, K-12, program 6, “Making Bread Together.”

7. In Ms. Mesmer’s classroom, students participate in a variety of fun activities to compare holidays, while learning about seasons and the earth’s rotation around the sun. See Social Studies in Action, A Teaching Practices Library, K-12, program 8, “Celebrations of Light.”

8. Watch students practice their French vocabulary using song, movement, and cut-and-paste activities in Teaching Foreign Languages, K-12: A Library of Classroom Practices, program 4, “Chicken Pox.”

9. A kindergarten class mixes with a 4th-grade class to create an original performance based on Quidam by Cirque du Soleil in The Arts in Every Classroom: A Video Library, K-5, program 11, “Students Create a Multi-Arts Performance.”

What are ways you are using play in your kindergarten classrooms?

Laughing and Learning with Limericks

WGBHTeaching Math K-4 LibThere once was a poet named Lear

Whose fondness for nonsense was dear.

His verses were short

And silly, of course.

And that’s why we fete him each year!

As I see it there are at least three good reasons to introduce your students to limericks this month:

1. May 12 was Edward Lear’s birthday and Limerick Day. Children today enjoy Lear’s sly sense of humor and the limerick’s manageable structure as much as the children for whom he wrote his verses in 1846. You can use the illustrated, closed-captioned audio book to introduce your students to the silly fun and rhyming challenges of limericks. Although limericks have a reputation for being bawdy or coarse, you can find many kid-friendly examples by searching limericks for children. Visit the Limerick Factory on Learner.org to give students practice with the form, permission to be goofy, and the urge to write their own poems.

2. Testing season is upon us and it’s likely you and your students could use a little comic relief. Humor is a healthful stress reliever. Sharing a limerick “moment” will take only a few minutes of class time. The resulting giggles (or groans) will be a refreshing break from test-itis. Provide students with a physical break as well by inviting them to stand up and clap their hands to the pronounced rhythm of a limerick.

3. Analyzing patterns in poetry is similar to recognizing patterns in mathematics. Using the Limerick Factory on Learner.org, you might have students devise codes for communicating the rhythmic and rhyming structures of limericks. Students who have not yet picked up on number patterns may benefit from the practice of finding patterns in accessible poems or nursery rhymes.

You can get a lot of brain-building mileage out of a five-line rhyming poem. May I challenge you to finish this one?

There once was a teacher named West

Whose students were scared of the test . . .

 

 

 

 

 

 

 

 

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.

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?

 

Valentine’s Day in the Elementary School Classroom

Teaching Math_Valentine's DayOn Valentine’s Day, engage your elementary students in math and language arts lessons that revolve around the holiday. Here are some resources:

Mathematics

Our Teachers’ Lab activity, How Many Valentines? offers a fun way to connect the Valentine’s Day holiday with elementary mathematics.

Observe a fun 4th-grade math lesson incorporating the Valentine’s Day theme in “Teaching Math: A Video Library, K-4,” program 42, “Valentine Exchange.”

Demonstrate reasoning and proof through the mystery of love with an interactive activity on the Teaching Math: Grades 3-5 Web site.

Language Arts

See how kindergarten teacher Cindy Wilson uses the making of Valentines as a means of promoting her students’ oral language skills in Teaching Reading K-2: A Library of Classroom Practices, program 2, “Building Oral Language.”

Linking Emotions and Mathematics

Neuro_2_emotion_mathIn many classrooms, math is a bunch of numbers and operations seemingly unrelated to what students do in their every day lives. Math is not typically thought of as an emotional subject, but emotions help solve problems. People apply what they’ve learned from past experiences in order to act advantageously in future situations. In order to motivate students to solve math problems, it’s important that your students care about the problems presented. Why is the problem relevant to them in their daily life?

In this short video “Emotions and Math” for unit 2 of Neuroscience & the Classroom, hear Prof. Abigail Bard explain how actively engaging the brain’s emotional centers should not be separated from academic information in the math classroom. Also, witness a teacher engage her students in the math lesson by drawing from their daily experiences.

Share here with other teachers how you connect your math (or other subject area) lessons to real world situations in order to engage your students.