Building a Positive Mathematics Community
Next week, on the afternoon of Thursday, April 30th, Eighth Grade students will present their Math Exhibitions. As always, parents and guests are invited, expected, and welcomed. There are many things that we do every year to confront students with academic challenge, recognize perseverant and collaborative problem solving, and encourage risk taking. The Math Exhibitions are just one of them. We so hope to see you there.
Given the occasion, now would be a great time to consider Mr. Lawrence's reflection on another math experience that happened not too long ago. Below is an excerpt of a recent article, written by Gary Lawrence and Hoyun Cho, that was taken from the April 2015 issue of Mathematics Teaching in the Middle School. It is for all who are growing to love math.
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The ability of students to learn mathematics with understanding is strengthened by a positive school environment (Hiebert and Grouws 2007). Such an environment depends on a classroom ethos. Just as important is the entire school community, in which all students are expected to learn through active participation and all teachers are expected to engage all students in mathematical tasks.
The environment should be one in which students are actively involved in doing mathematics. Challenging problems should be posed, and the school environment should encourage students to work on them individually and in groups. Sometimes students will need to work for extended periods of time, and often they should encounter unfamiliar topics. These students should be encouraged to develop such traits and habits of mind as perseverance, cooperative work skills, reflection, self-assessment, self-confidence, decision making, and risk taking (Cuoco, Goldenberg, and Mark 1996; Goldenberg and Shtein- gold 2003). All these elements will be keys to their success in mathematics. This article recounts how one small urban school in northern New Jersey developed a school environment that created a positive mathematics culture.
love math. The panelists share their
educational and professional experiences and discuss how mathematics
contributes to their work and personal
lives. Students in grades 6 through 8
are encouraged to ask questions during the panel discussion to guide the
guests’ comments.
As I Love Math Day has become more established, we have broadened our reach to find panelists. Recently, one panelist was an associate professor of history who specializes in the history of mathematics education as well as women in science. She works with the Smithsonian Institution, cataloguing mathematical instruments for its website. Another panelist was the grandfather of several students who has taught at the middle school, high school, and college levels his entire career. He traveled 1500 miles to our school to share his passion for geometry, specializing in visual and reflective relationships. Paper folding, mirror applications, kaleidoscopes, and Platonic and Archimedean solids held particular interest for him. We have also invited alumni. One alumna had become an assistant editor for a medical journal. Another traveled from Texas, where he worked as an oil trader. Both shared stories about math in the workplace.
Distinguished panelists such as these spend February 14 visiting classes, sharing their expertise and their passions, answering questions from the students, and celebrating the excellent work that students at all grade levels do in mathematics at the school.
To offer younger students a taste of
what is to come, we always find two
or three problems that are appropri-
ate for the students in fourth and fifth
grades. These students spend several days working on each problem, and
they also turn in submissions to be
judged by a panel. They are encouraged to collaborate with parents,
friends, and teachers . . .
With several weeks of problem
solving under their belts, students
are ready for all the celebrations
that occur on I Love Math Day. All
day long, students from preschool
through eighth grade will be thinking about math problems, playing math games, and doing all kinds of activities that involve counting and making patterns and every form of mathematical undertaking. Adults who love math and who use it in their careers and hobbies will be visiting the school. Students who participated
in the problem-solving activities will
have opportunities to share their best
submissions and explain their think-
ing with fellow students and adults.
Given the occasion, now would be a great time to consider Mr. Lawrence's reflection on another math experience that happened not too long ago. Below is an excerpt of a recent article, written by Gary Lawrence and Hoyun Cho, that was taken from the April 2015 issue of Mathematics Teaching in the Middle School. It is for all who are growing to love math.
_____________________________________
The ability of students to learn mathematics with understanding is strengthened by a positive school environment (Hiebert and Grouws 2007). Such an environment depends on a classroom ethos. Just as important is the entire school community, in which all students are expected to learn through active participation and all teachers are expected to engage all students in mathematical tasks.
The environment should be one in which students are actively involved in doing mathematics. Challenging problems should be posed, and the school environment should encourage students to work on them individually and in groups. Sometimes students will need to work for extended periods of time, and often they should encounter unfamiliar topics. These students should be encouraged to develop such traits and habits of mind as perseverance, cooperative work skills, reflection, self-assessment, self-confidence, decision making, and risk taking (Cuoco, Goldenberg, and Mark 1996; Goldenberg and Shtein- gold 2003). All these elements will be keys to their success in mathematics. This article recounts how one small urban school in northern New Jersey developed a school environment that created a positive mathematics culture.
I LOVE MATH DAY
Every year, the school celebrates I Love Math Day on February 14. On this day, students enjoy math-related activities and recognize excellent student work after solving challenging problems. In the weeks leading up to the event-filled day, middle school students work in small teams to solve four intriguing, rich, mathematics problems. They are given one week to solve each problem and prepare a solution to submit to judges. Submis- sions can be in the form of an essay, a slide show, a video, a poster, a game, or a dramatization.
Every year, the school celebrates I Love Math Day on February 14. On this day, students enjoy math-related activities and recognize excellent student work after solving challenging problems. In the weeks leading up to the event-filled day, middle school students work in small teams to solve four intriguing, rich, mathematics problems. They are given one week to solve each problem and prepare a solution to submit to judges. Submis- sions can be in the form of an essay, a slide show, a video, a poster, a game, or a dramatization.
Through an I Love Math blog,
teachers encourage all school families
to attempt to solve each problem together and join in the fun. They hope
that parents and students in all grades
will not only discuss and puzzle over
these problems but also enjoy the
pursuit of a solution together. In one
classic problem, students were asked
to create a visual demonstration of the Pythagorean theorem. Another
problem was based on a centuries-old
Middle Eastern story, which asked
students to settle a family dispute over
a bequest of camels.
Another highlight of I Love Math Day is a panel discussion introducing two or three adult guests who
Another highlight of I Love Math Day is a panel discussion introducing two or three adult guests who
When assembling a panel for the
first time, it is usually best to keep it simple and organic. Parents in the school community are one of the best
sources of panelists. It is fun to help
students see that almost every adult
uses math productively. Within our
parent community, we have found
cooks, bookkeepers, architects, and
artists to serve on the panel. Sometimes parents speak about a leisure
pastime that uses math: baseball and
statistics, travel and foreign currencies. Grandparents work splendidly as
math resources, as well. One grand-
parent was a carpenter, another was a retired teacher, and another was a judge. Almost any connection to
mathematics can work. More creative
connections lead to more inspiring
events.
As I Love Math Day has become more established, we have broadened our reach to find panelists. Recently, one panelist was an associate professor of history who specializes in the history of mathematics education as well as women in science. She works with the Smithsonian Institution, cataloguing mathematical instruments for its website. Another panelist was the grandfather of several students who has taught at the middle school, high school, and college levels his entire career. He traveled 1500 miles to our school to share his passion for geometry, specializing in visual and reflective relationships. Paper folding, mirror applications, kaleidoscopes, and Platonic and Archimedean solids held particular interest for him. We have also invited alumni. One alumna had become an assistant editor for a medical journal. Another traveled from Texas, where he worked as an oil trader. Both shared stories about math in the workplace.
Distinguished panelists such as these spend February 14 visiting classes, sharing their expertise and their passions, answering questions from the students, and celebrating the excellent work that students at all grade levels do in mathematics at the school.
HOW TEACHERS PREPARE THE ACTIVITIES
Every year, the school searches out good problems that will challenge students and keep them interested and working hard for a week or more. Ideally, the problems require a creative use of middle school level mathematics ideas like factors, prime numbers, the Pythagorean theorem, squares, and square roots. The problems also prompt students to perform the fundamental tasks of all skilled mathematicians: ask questions; collaborate with peers; use appropriate resources; draw pictures; make models; and try, fail, and try again. Challenging problems are drawn from textbooks; articles; periodicals; current popular math books; and collections of problems, puzzles, comics, and cartoons . . .
Students tackle these problems with relish. Sometimes the sixth graders are hesitant, unsure how to work in small groups on a problem that seems beyond their level of understanding. By eighth grade, those same students cannot wait to tackle each problem, figure out how to make some progress, and prepare a submission for the judges. Students understand that each problem will be demanding and will require persistence and creativity. They also know that they can discuss these problems with their parents and teachers. Internet research is permitted. Anything that mathematicians would do is encouraged. Of course, like good mathematicians, they cannot present the work of others as their own. If they receive help, the help should be acknowledged, and the students need to submit a solution that demonstrates their own mastery of the problem and the math concepts involved.
Every year, the school searches out good problems that will challenge students and keep them interested and working hard for a week or more. Ideally, the problems require a creative use of middle school level mathematics ideas like factors, prime numbers, the Pythagorean theorem, squares, and square roots. The problems also prompt students to perform the fundamental tasks of all skilled mathematicians: ask questions; collaborate with peers; use appropriate resources; draw pictures; make models; and try, fail, and try again. Challenging problems are drawn from textbooks; articles; periodicals; current popular math books; and collections of problems, puzzles, comics, and cartoons . . .
Students tackle these problems with relish. Sometimes the sixth graders are hesitant, unsure how to work in small groups on a problem that seems beyond their level of understanding. By eighth grade, those same students cannot wait to tackle each problem, figure out how to make some progress, and prepare a submission for the judges. Students understand that each problem will be demanding and will require persistence and creativity. They also know that they can discuss these problems with their parents and teachers. Internet research is permitted. Anything that mathematicians would do is encouraged. Of course, like good mathematicians, they cannot present the work of others as their own. If they receive help, the help should be acknowledged, and the students need to submit a solution that demonstrates their own mastery of the problem and the math concepts involved.
FEBRUARY 14: THE BIG DAY ARRIVES
Middle school students will meet
a panel of two or three visiting adults
who love math. They will hear the
different ways that these adults use
math in their jobs and in their other
pursuits. Students will have an opportunity to ask the panelists questions,
and students and panelists together
participate in playful guessing games:
An assembly after the panel discussion also provides an opportunity to give prizes and awards for the excel- lent mathematical work the students did in the problem-solving activities. Awards are given for the most creative solutions, the best explana- tion of a solution, the best teamwork, the most vivid video presentation,
the most beautiful poster, and so on. The categories for awards should be varied and playful, the point being to publicly recognize great mathematical work in all its variety. Awards can be simple treats, candy bars, age- appropriate math books, math oriented calendars, and so on. A valentine is also appropriate because it is, after all, Valentine’s Day.
- How many jelly beans are in a one-gallon jar?
- Will the guesses form a standard distribution around the correct answer? (Usually not)
- Will the adult mathematicians be better guessers? (Again, usually not) • Why are the adult mathematicians such poor guessers?
An assembly after the panel discussion also provides an opportunity to give prizes and awards for the excel- lent mathematical work the students did in the problem-solving activities. Awards are given for the most creative solutions, the best explana- tion of a solution, the best teamwork, the most vivid video presentation,
the most beautiful poster, and so on. The categories for awards should be varied and playful, the point being to publicly recognize great mathematical work in all its variety. Awards can be simple treats, candy bars, age- appropriate math books, math oriented calendars, and so on. A valentine is also appropriate because it is, after all, Valentine’s Day.
I LOVE MATH DAY GROWS
MATHEMATICIANS
I Love Math Day has become a key element in Mustard Seed School’s pursuit of a distinctive mathematics culture. With February 14 as a focal point, the students commit several weeks to working on rich, challenging problems. Through the effort to solve these problems, they grow as mathematicians. They seek to make sense of problems, develop strategies, critique strategies, work collaboratively, and create and test hypotheses. When they approach a solution, they spend additional time finding ways to explain their thinking and justify their solutions. Through creative presentations, they continue to reflect on mathematical content long after they find a solution. These important skills and traits will help students develop into proficient mathematicians. The celebratory culmination of their work provides an opportunity to continue thinking and talking about their work and engaging with adults who use math in their professions and in their leisure pursuits.
I Love Math Day has become a key element in Mustard Seed School’s pursuit of a distinctive mathematics culture. With February 14 as a focal point, the students commit several weeks to working on rich, challenging problems. Through the effort to solve these problems, they grow as mathematicians. They seek to make sense of problems, develop strategies, critique strategies, work collaboratively, and create and test hypotheses. When they approach a solution, they spend additional time finding ways to explain their thinking and justify their solutions. Through creative presentations, they continue to reflect on mathematical content long after they find a solution. These important skills and traits will help students develop into proficient mathematicians. The celebratory culmination of their work provides an opportunity to continue thinking and talking about their work and engaging with adults who use math in their professions and in their leisure pursuits.
REFERENCES
Cuoco, Al, E. Paul Goldenberg, and June Mark. 1996. “Habits of Mind: An Or- ganizing Principle for a Mathematics Curriculum.” Journal of Mathemati- cal Behavior 15 (4): 375–402.
Goldenberg, E. Paul, and Nina Shteingold. 2003. “Mathematical Habits of Mind.” In Teaching Mathematics through Problem Solving: Prekindergarten–Grade 6, edited by Frank K. Lester Jr. and Randall I. Charles. Reston, VA: National Council of Teachers of Mathematics.
Hiebert, James, and Douglas A. Grouws. 2007. “The Effects of Classroom Mathematics Teaching on Students’ Learning.” In Second Handbook of Research on Mathematics Teaching and Learning, edited by Frank Lester Jr. Charlotte, NC: Information Age.
Cuoco, Al, E. Paul Goldenberg, and June Mark. 1996. “Habits of Mind: An Or- ganizing Principle for a Mathematics Curriculum.” Journal of Mathemati- cal Behavior 15 (4): 375–402.
Goldenberg, E. Paul, and Nina Shteingold. 2003. “Mathematical Habits of Mind.” In Teaching Mathematics through Problem Solving: Prekindergarten–Grade 6, edited by Frank K. Lester Jr. and Randall I. Charles. Reston, VA: National Council of Teachers of Mathematics.
Hiebert, James, and Douglas A. Grouws. 2007. “The Effects of Classroom Mathematics Teaching on Students’ Learning.” In Second Handbook of Research on Mathematics Teaching and Learning, edited by Frank Lester Jr. Charlotte, NC: Information Age.
Hoyun Cho, hcho1416@capital.edu,
is an assistant professor of education (mathematics education) in the Depart- ment of Education at Capital University, Columbus, Ohio. He works with elemen- tary, middle, and high school mathemat- ics preservice teachers and is interested in developing instructional tasks that promote prospective teacher’s thinking and learning.
Gary D. Lawrence, glawrence@mustardseedschool.org, holds the Coleman Fung Chair for Mathematics at Mustard Seed School, an independent pre-K–grade 8 school in Hoboken, New Jersey. He teaches seventh-grade prealgebra and eighth- grade algebra and is especially interest- ed in developing students’ love of mathe- matics through problem solving, student exhibitions, and cartoon activities.
is an assistant professor of education (mathematics education) in the Depart- ment of Education at Capital University, Columbus, Ohio. He works with elemen- tary, middle, and high school mathemat- ics preservice teachers and is interested in developing instructional tasks that promote prospective teacher’s thinking and learning.
Gary D. Lawrence, glawrence@mustardseedschool.org, holds the Coleman Fung Chair for Mathematics at Mustard Seed School, an independent pre-K–grade 8 school in Hoboken, New Jersey. He teaches seventh-grade prealgebra and eighth- grade algebra and is especially interest- ed in developing students’ love of mathe- matics through problem solving, student exhibitions, and cartoon activities.