Joshua Bright for The New York Times Museum of Mathematics “Harmony of the Spheres,” one of the exhibits, being tested before opening day.
Overview | How is mathematics beautiful? How can the beauty and elegance of mathematics be communicated?
In this lesson, students read about the new Museum of Mathematics and its mission to convey the beauty of mathematics through fun and engaging exhibits. Then, students explore mathematics by designing and producing their own exhibit that communicates the beauty and elegance of this creative discipline.
Materials | Computers with Internet access; craft materials
Warm-Up | Begin by asking students to make a short list of things that people consider beautiful. Have a quick share out, and then ask the students if anyone has something that might be considered mathematical on their list. Ask students to then make a short list of some mathematical things that might be considered beautiful.
Ask students to share their conceptions of beautiful mathematics. If there are students who could not think of anything for their list, have other students who could attempt to convey the beauty of their choices. Ask students to ponder the questions “How might we convey the beauty of mathematics?” and “Why might it be good to spread the idea that mathematics is beautiful?”
Related | Have students read this review of the new Museum of Mathematics, a museum with a mission to convey the beauty and fun of math. Edward Rothstein writes:
Questions | For discussion and reading comprehension:
Kenneth Chang/The New York Times Look at the metal bands that wrap around the cylindrical walls on Manhattan rooftop water tanks. They are much closer together near the bottom of the tanks than at the top. Why? Go to related article “Water Tanks, Fire Hydrants and Math” »
Activity | In this activity students produce their own exhibits that demonstrate the fun and beauty of mathematics. One option would be to have a single theme for the class exhibit, say, tilings, and then have small groups of students each work to produce a mathematical piece, or pieces, that fit the theme. Alternatively, small groups could each choose a different theme, and the exhibit could offer a variety of mathematics to appreciate.
Present students with the suggestions below and invite them to do further independent research to find other ways they might demonstrate mathematical beauty. In addition to creating the pieces for the exhibit, have each group title their work and produce a written explanation of what they have done, how they did it, and what mathematics is being demonstrated.
Here are some suggested exhibit ideas:
Tilings of the Plane
A tiling of the plane is created by arranging congruent polygons in a repeating pattern so as to cover the entire plane. Just as a floor or wall can be intricately designed using squares, triangles or hexagons, tilings of the plane can be very beautiful, and of course are highly mathematical. Have students take a look at some of the basic tilings of the plane, and have groups create and decorate their own tilings. Be sure to have students explain the math about why their tiling works and how they know it can be continued indefinitely.
Geometric Art
Have students browse the minimal geometric art at Geometry Daily. This work is simple, beautiful and mathematical, and can serve as inspiration for students to turn their homework diagrams into their own works of mathematical art.
Or have students play around with the free, online graphing utility Desmos to turn the graphs of mathematical functions into beautiful pictures. See the Desmos art gallery for ideas.
Math Photographs
Have students take pictures of the math they see all around them. Have them title their pieces and provide a short, written explanation of the mathematics captured in their photographs.
To go even further, have students load their photographs into a mathematics software package like Geogebra and plot the mathematical curves inherent in their images. Be sure the students narrate both their creative and mathematical processes.
Mathematical Sculptures
Have students create a mathematical sculpture gallery full of paper polyhedra, sliceforms or gumdrop solids. Or have them explore the highly mathematical world of origami, like in this exhibit at the Institute for Figuring.
When all of the exhibits are complete, have a gallery walk so that everyone can admire and appreciate the beautiful mathematics that has been created. Invite other math teachers and classes to visit and participate, and if the opening goes well, make it into a yearly math and art festival like this Brooklyn school has done.
Joshua Bright for The New York Times The “String Product,” an interactive calculator based on a paraboloid, fills the staircase at the new Museum of Mathematics in Manhattan. Go to related article “Opening the Doors to the Life of Pi” »
Going Further | Below are two additional ideas for math teachers related to this lesson:
1. MoMath Exhibits and Puzzles: Have students check out MoMath’s Web site, their gallery of photos and their YouTube channel to see what’s going on at the Museum of Mathematics. Have them research the mathematics behind the exhibits and present their findings to the class. And check out some of the MoMath-themed puzzles from the Wordplay blog, like these inspired by the Museum’s exhibits and these from the MoMath Masters tournament.
2. Art and Mathematics: The Bridges Organization’s annual conference explores the connections between art and mathematics Have students peruse the art gallery for this year’s conference, select a mathematical artist to profile and prepare a short presentation about the artist, their art and the mathematics behind it.
Common Core Mathematics Standards, 6-12
Geometry Standards
Understands congruence in terms of rigid motion.
Makes geometric constructions.
Applies geometric concepts in modeling situations.
Practices
Use appropriate tools strategically.
In this lesson, students read about the new Museum of Mathematics and its mission to convey the beauty of mathematics through fun and engaging exhibits. Then, students explore mathematics by designing and producing their own exhibit that communicates the beauty and elegance of this creative discipline.
Materials | Computers with Internet access; craft materials
Warm-Up | Begin by asking students to make a short list of things that people consider beautiful. Have a quick share out, and then ask the students if anyone has something that might be considered mathematical on their list. Ask students to then make a short list of some mathematical things that might be considered beautiful.
Ask students to share their conceptions of beautiful mathematics. If there are students who could not think of anything for their list, have other students who could attempt to convey the beauty of their choices. Ask students to ponder the questions “How might we convey the beauty of mathematics?” and “Why might it be good to spread the idea that mathematics is beautiful?”
Related | Have students read this review of the new Museum of Mathematics, a museum with a mission to convey the beauty and fun of math. Edward Rothstein writes:
The goal, each principal emphasized in conversations this week, was to show that math was fun, engaging, exciting. MoMath is a proselytizing museum. And despite its flaws, it is exhilarating to see math so exuberantly celebrated. And while fourth through eighth are said to be the intended grade levels, it is hard to imagine a younger child or mature adult not drawn in by some exhibits here. In many ways the sensations of the displays are more compelling than the explanations of their content.Read the entire article with your class, and then answer the questions below.
Questions | For discussion and reading comprehension:
- What are the goals of the Museum of Mathematics?
- What are some of the exhibits at the Museum of Mathematics?
- What are some of the difficulties in designing exhibits for a math museum?
- What does the author enjoy about the best exhibits at the museum?
- How does the author think some exhibits could be improved?
Kenneth Chang/The New York Times Look at the metal bands that wrap around the cylindrical walls on Manhattan rooftop water tanks. They are much closer together near the bottom of the tanks than at the top. Why? Go to related article “Water Tanks, Fire Hydrants and Math” »RELATED RESOURCES
From The Learning Network
From NYTimes.com
- One Math Museum, Many Variables
- New Museum of Mathematics: Where Math is Cool
- Numberplay: Math as a Spectator Sport
Around the Web
Activity | In this activity students produce their own exhibits that demonstrate the fun and beauty of mathematics. One option would be to have a single theme for the class exhibit, say, tilings, and then have small groups of students each work to produce a mathematical piece, or pieces, that fit the theme. Alternatively, small groups could each choose a different theme, and the exhibit could offer a variety of mathematics to appreciate.
Present students with the suggestions below and invite them to do further independent research to find other ways they might demonstrate mathematical beauty. In addition to creating the pieces for the exhibit, have each group title their work and produce a written explanation of what they have done, how they did it, and what mathematics is being demonstrated.
Here are some suggested exhibit ideas:
Tilings of the Plane
A tiling of the plane is created by arranging congruent polygons in a repeating pattern so as to cover the entire plane. Just as a floor or wall can be intricately designed using squares, triangles or hexagons, tilings of the plane can be very beautiful, and of course are highly mathematical. Have students take a look at some of the basic tilings of the plane, and have groups create and decorate their own tilings. Be sure to have students explain the math about why their tiling works and how they know it can be continued indefinitely.
Geometric Art
Have students browse the minimal geometric art at Geometry Daily. This work is simple, beautiful and mathematical, and can serve as inspiration for students to turn their homework diagrams into their own works of mathematical art.
Or have students play around with the free, online graphing utility Desmos to turn the graphs of mathematical functions into beautiful pictures. See the Desmos art gallery for ideas.
Math Photographs
Have students take pictures of the math they see all around them. Have them title their pieces and provide a short, written explanation of the mathematics captured in their photographs.
To go even further, have students load their photographs into a mathematics software package like Geogebra and plot the mathematical curves inherent in their images. Be sure the students narrate both their creative and mathematical processes.
Mathematical Sculptures
Have students create a mathematical sculpture gallery full of paper polyhedra, sliceforms or gumdrop solids. Or have them explore the highly mathematical world of origami, like in this exhibit at the Institute for Figuring.
When all of the exhibits are complete, have a gallery walk so that everyone can admire and appreciate the beautiful mathematics that has been created. Invite other math teachers and classes to visit and participate, and if the opening goes well, make it into a yearly math and art festival like this Brooklyn school has done.
Joshua Bright for The New York Times The “String Product,” an interactive calculator based on a paraboloid, fills the staircase at the new Museum of Mathematics in Manhattan. Go to related article “Opening the Doors to the Life of Pi” »1. MoMath Exhibits and Puzzles: Have students check out MoMath’s Web site, their gallery of photos and their YouTube channel to see what’s going on at the Museum of Mathematics. Have them research the mathematics behind the exhibits and present their findings to the class. And check out some of the MoMath-themed puzzles from the Wordplay blog, like these inspired by the Museum’s exhibits and these from the MoMath Masters tournament.
2. Art and Mathematics: The Bridges Organization’s annual conference explores the connections between art and mathematics Have students peruse the art gallery for this year’s conference, select a mathematical artist to profile and prepare a short presentation about the artist, their art and the mathematics behind it.
Common Core Mathematics Standards, 6-12
Geometry Standards
Understands congruence in terms of rigid motion.
Makes geometric constructions.
Applies geometric concepts in modeling situations.
Practices
Use appropriate tools strategically.
댓글 없음:
댓글 쓰기