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“Polynomial functions!”

“Trig identities!”

“How about the properties? Commutative, associative, distributive.”

So unfolded a laundry list of what a group of math teachers considered the more painful and less necessary concepts covered in the average high school math curriculum.

The laments, aired at EduCon 2.5 in Philadelphia at Science Leadership Academy last weekend, were part of a discussion around how to rebuild math instruction under the radically different—and admittedly unlikely—parameters posed by moderator Mike Thayer, a math teacher at Summit Public Schools in New Jersey.

Thayer, who also has a background teaching high school physics, proposed a scenario in which high school freshmen would take a one-year course (or a one-semester course in a block scheduling system) that covered the essentials of Algebra 1 and 2, Geometry, and possibly parts of Trigonometry. Any additional math concepts might be learned in a cross-disciplinary fashion through other courses. For example, chemistry teachers would be responsible for teaching

students the basics of logarithms while covering the pH scale. Biology teachers would explain concepts of exponential growth to their students when discussing species population and reproduction.

The rationale of such a course, Thayer said, would be to create a version of math instruction that more fully lives with the inquiry-based learning approach embraced by the Science Leadership Academy, the public magnet high school where the conference took place. His vision—which hinges on what he concedes is a large assumption that students would enter high school competent in basic computational thinking—is for a course that would both streamline a high school student’s general math experience, and empower and encourage them to learn additional math skills to solve real-world problems of their own interest.

As one teacher at the discussion put it: “I’d like to delete polynomial functions, but I’d like my students to see a roller coaster and think, ‘There must be math involved in that,’ and to go online and try and figure that out.”

Thayer asked the teachers to consider four questions as they imagined the hypothetical course:

1. WHAT STAYS AND WHAT GOES? Consider both what concepts would get more or less emphasis, as well as what method of learning (lectures, work sheets, group work, collaborative projects, etc.) would work best.
2. NEXT STEP FOR STUDENTS? Options could include more advanced mathematics courses, independent mathematics projects, courses in other subjects that included applicable advanced math concepts, or some combination.
3. HOW WOULD TEACHING CHANGE? Choose which lessons you’d save and which lessons you’d skip. Envision whether you’d use the same kinds of exercises to develop students skills, and whether you’d structure class time in the same manner, or perhaps utilize it differently.
4. WHAT WOULD YOU ASSESS? Tests should reflect the purpose of the course, to develop students’ understanding of the theoretical and practical purposes of math.

Most of the discussion during the 90-minute talk focused on the first two points, and the group generally agreed the course would need to focus on changing student thought processes.

“What I am hearing is that if we would like to really make math meaningful for our students, we need to do things to create the ability for them to be truly mathematical thinkers,” Thayer said at one point after hearing a few responses.

There were, however, disagreements over the relative importance of concepts. And a couple of teachers even asked whether geometry would fit within the parameters of such a course.

The group also questioned whether a focus on real-world math applications would be the most likely way to spur students into independent investigation, and whether that focus could create an unintended bias in the kind of material covered. As an example, teachers noted that using tools like 101 Questions, a website that asks users to think of a question related to a displayed image, could result in an excessive focus on proportionality.

Thayer encouraged such discourse, suggesting it would be essential in his new model.

“I think the first thing for us, in order to be masters in context as well as content, is to recognize our strengths and weaknesses,” he said. “I would love for somebody else to be able to come into my classroom and explain why [a concept] is important.”

In a speech at EduCon earlier that morning, Philadelphia public schools Superintendent William Hite stressed the need for teachers to move from content to context expertise. And in a later discussion, Science Leadership Academy founding Principal Chris Lehmann conceded such an approach could be more difficult in a math classroom, but not impossible.

Thayer, meanwhile, warned that if math teachers didn’t find a way to make that difficult shift, they could be marginalized.

“Most of the stuff we teach” in traditional courses, he said, “the Khan Academy does it for free.”

PBS NewsHour

By Rebecca Jacobson

Carrie Lewis and Kelly Steele’s fifth grade students slide and spin across the classroom floor, doing the hustle, the robot, and the running man. While it may look at first glance like goofing off, these students are actually dancing for a higher cause…math.

Lewis, a STEM specialist for Virginia’s Lynchburg city schools, and Steele, who teaches gifted education in Bedford county, Virginia, are both math enthusiasts eager to instill in their students a love of the subject. And dancing, they hoped, might be just the thing to help tackle a common fifth-grade learning deficit — number patterns.

“Dances are patterns,” Lewis said. “We had identified that our students had trouble with patterns and this was a way to get them involved in it.”

Both teachers are part of Sweet Briar College’s STEM teacher education program, where they worked together to design “dance by numbers,” a lesson plan that relies on dance to teach pattern recognition. In the video above, Lewis explains how the lesson works.

IDENTIFYING A PATTERN

The first step was to turn a dance routine into a number pattern. Students logged onto the Pillsbury Dough Boy website and watched, studied and deconstructed the cartoon mascot’s six dance moves. They assigned each step a number, and charted the patterns in his dance.

“Once they translated the number to a movement, they began to see how it would be really easy to get a pattern,” Lewis said. “I had them watch ‘America’s Best Dance Crew’ so they could see that they’re just doing the same thing over and over again.”

MAKING THEIR OWN MOVES 

The students then choreographed their own dance routines. The teachers required that each routine contain at least five moves that repeated at least once. Songs were to be set to instrumental music of the students’ choice — some opted for hip-hop; others for the Mario Bros theme.

Using stopwatches to clock the average time of their routine, students were asked to then calculate how many times their pattern would repeat throughout the course of the song, and then turn the resulting data into a graph.

“If your song is 100 seconds, how many repetitions will you do of your dance?,” Steele said. “If you use the extended version of your dance, 200 seconds, how many repetitions do you need to do? They are using their graph to figure that information out.”

ANALYZING THE DANCE 

Finally, each group performed their original routine for their classmates. And midway through the dance, they’d freeze, and the class would be asked to predict the next move in the pattern. (Lewis called these “jump-ins.”)

In addition to patterns and graphing, the dance lesson helps students with averaging and calculating elapsed time, along with multiplication and division.

“If their pattern was seven [steps] long and they were asked what jump-in 23 was, rather than sit there and count, count, count, they realized they could do multiples,” Lewis said. “You could almost see that light bulb go on.”

“Dance by numbers” received enthusiastic feedback from a regional conference for STEM teachers, said Arlene Vinion-Dubiel at Sweet Briar College, who helped the teachers implement their lesson plan.

And inside the classroom, results were tangible. Math test scores went up. Shy students happily break-danced at the front of the class. One group performed their routine for the school talent show last year.

“They were 100% into it,” Steele said, who expected the boys in her rural classes wouldn’t dance in front of their peers.

“Math is such a challenge,” Lewis added. “What you’re trying to teach them is that what they’re learning isn’t isolated to a work sheet. That’s what STEM is all about — letting the measurements or the math speak to you and letting it teach you something.”

Watch the students in action here:

http://youtu.be/ssmB_MtgJ_k

Via PBS NewsHour.

Re-Roofing Your Uncle's House

By Almetria Vaba

Math can be made meaningful when connected to students’ experiences. With video clips and interactive games from public media students practice math concepts while exploring real world concepts. Learn how to decorate an intricate cake, play the role of the pharmacist, roof a house and more using PBS LearningMedia resources to measure with math.

Using Recipes for Fractions Lesson Plan and Video
While doubling a cupcake recipe, students practice three ways of doubling fractions using representations, addition, and multiplication. Students also convert between improper fractions and mixed numbers. Grades 4-8.

Re-Roofing Your Uncle’s House Interactive Game
In this interactive activity adapted from the Wisconsin Online Resource Center, students use mathematics and measuring skills to solve a construction problem by playing a game using tools (including a tape measure, notepad, and calculator) to determine how many shingles are needed to reroof a house. Students also learn the importance of proper planning and how miscalculating the amount of materials necessary can add to the cost and time spent on a project. Grades 3-9.

Cake Designer Video
Math made delicious! In this video, a cake designer describes how she uses math with her recipes and designs. Students can relate the importance of mathematics to the field of cake designing. Grades 3–9.

Area of Circles with Dive Dog Interactive Game
In this animated activity students learn the formula for the area of a circle and then apply it to multiple scenarios involving Spot the Dog. Activities include solving problems involving the area of a circle and for the areas of parallelograms, triangles, and circles. Students also calculate the area of a circle using the formula and recognize the relationship between a circle’s diameter and its circumference. Grades 7-8

Dunk Tank: Area of Squares & Rectangles Video and Interactive Games
Using a combination of video and interactive gaming, each game addresses a single topic in the 6th grade math curriculum and students compete with themselves for high scores. Other Dunk Tank episodes include: Venn Diagrams; Mean, Median, Mode & Range; Ratio & Proportion; Fractions, Decimals & Percents; Liquid Volume; and Circles. Grade 6

Ian Hill/Thinkstock/Penguin

By Nikhil Goyal

Call it “The Triumph of Nerds.” Poll statisticians have risen to rock star status. One of the most famous is New York Times’ wunderkind Nate Silver — or as Jon Stewart put it, “Lord and god of the algorithm.” He may be best known for predicting the 44th president, but Silver could be the one man who can save mathematics education in America.

Silver, who first gained notoriety for forecasting the performance of Major League Baseball players and for correctly predicted the winner of 49 of 50 states in the 2008 election, can save the tattered reputation of math subjects.

For students across the country, there’s clearly an engagement deficit in the subject. Paul Lockhart, a math teacher in New York, writes in A Mathematician’s Lament [PDF] that if he had to design a system for the express purpose of destroying a child’s natural curiosity and love of pattern-making, he couldn’t possible do a better job than is currently being done. He explains that he simply wouldn’t have the “imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education.”

Across the land, kids hate math. You can hear it in their constant groans and see it in their deranged faces. They ask their teachers, “When am I ever going to use this in life?” On most occasions, they never will. Even President Obama agrees. He recently said on the Tonight Show, “The math stuff I was fine with until seventh grade. Malia is now a freshmen in high school and I’m pretty lost. It’s tough.” And no wonder — the system is suffering from a tragic case of nostalgia. The origins of the current curriculum draw back to 1892 when the Committee of Ten hashed out a standard curriculum, which would eventually be adopted almost unanimously by schools.

As a result, the potential to love and embrace math is being squandered — perhaps even the future of potential Nate Silvers and Nobel Laureates. As students progress from grade to grade, many start losing interest in math.

There are lots of reasons for this. In the current system, students’ confidence in their math abilities becomes undermined, according to a Duke University study. Math is taught as computation rather than a means of exploration and discovery. Instead of engaging in meaningful problems and learning in depth rather than breadth, kids are assigned frivolous, repetitive problems. And finally, the way math is generally taught has no relevance to real life. School has become a practice of learning tricks for the test one week and forgetting the next. In elementary schools, kids come to understand that they’re expected to follow directions, fill out worksheets, and master a set of concepts.

Our process of transferring from subject to subject in math is also broken. The curriculum pyramid is founded on arithmetic and algebra, all building up to one subject — at the top of the pyramid is calculus. While mathematicians, engineers, physicists, and particular scientists use calculus in meaningful ways, in their day-to-day lives, most people do not. Ironically, M.I.T. graduates, who are trained in science and mathematics, said in a survey regarding their daily use of math that most use nothing more than arithmetic, statistics, and probability.

Sol Garfunkel and David Mumford in a New York Times Op-Ed summed it up nicely: “Imagine replacing the sequence of algebra, geometry and calculus with a sequence of finance, data and basic engineering. In the data course, students would gather their own data sets and learn how, in fields as diverse as sports and medicine, larger samples give better estimates of averages.” Clifford Konold, a professor at the University of Massachusetts, counted data displays in The New York Times and found that in 1972, there were four graphs or tables in 10 consecutive weekday editions, excluding the sports and business sections. There were eight in 1982 and 44 in 1992. Next year, he could find more than 100. His conclusion: statistical reasoning is an indispensable skill.

Fortunately, many universities are scrambling to teach statistics and probability, especially through sports. In one class at James Madison University, students used the example of Steve Nash of the Phoenix Suns and free throws to learn the probability of coin tosses. Last year’s hit film Moneyball popularized the power of probability from predicting division standings to on-base percentages.

Just weeks after the election, Nate Silver’s Triumph of the Nerds, his renowned legacy and dedication to numbers, has the potential to telegraph an important message to kids: It’s O.K. to be a math nerd. Numbers can actually mean something in the grand scheme of things. We need more people who can number crunch and predict and prize math.

If parents and teachers use Silver’s groundbreaking work to talk to young people about civics, polls, statistics, and numbers, the power and beauty of mathematics, kids can experience this fascinating subject could be experienced in a whole new way.

Nikhil Goyal is a senior at Syosset High School in Woodbury, New York, and the author of One Size Does Not Fit All: A Student’s Assessment of School.

As schools start experimenting with educational software — or blended learning — teachers are trying to find ways of using tech to enhance learning in different subjects. When it comes to math, specifically, the tactics vary widely — from using software for remediation, to practicing drills and exercises to move students ahead at their own pace, to completely re-conceptualizing the traditional classroom model.

The one underlying common thread? Using online math has begun to change teachers’ perspectives. Here’s how blended learning in math is taking shape in three California schools.

BREAKING DOWN WALLS

Two Summit charter schools in San Jose, Calif. provide examples of blended learning that completely deconstruct the traditional classroom model. Just opened last year, Rainier and Tahoma have taken advantage of their one-to-one computer program to experiment with Khan Academy videos for math instruction. When the program first began, teachers introduced a concept, then had students do practice exercises using Khan Academy, which also provided assessment results for the teacher.

“I liked that model because it freed me up to do high-quality targeted instruction,” said Zack Miller a math teacher.

But Miller found this model unsatisfying in some ways. The ninth-grade class was working at more or less the same pace, with the only differentiation being the varying levels. “My biggest struggle last year was I had too many different skill levels in there and I had to kind of teach to one pace,” Miller said. “I kept thinking, ‘If I could only break down the walls.’”

This year, that’s exactly what Summit Rainier and Tahoma did. They’ve built one large math room for 200 kids, with smaller rooms branching off the main room that are set aside for assessments, projects and individual tutoring. Teachers work in teams of seven, alternating between teaching mini-lessons at the “tutoring bar,” roaming around the room offering help and supervising more in-depth projects designed for applying concepts students have learned.

It sounds chaotic, but Miller prefers it. Students at Rainier and Tahoma have individualized lesson plans that are not related to their grade level. In a typical day, students come in and check the schedule for the goal they should be working on that day. Then, if the mini-lesson on that skill is scheduled, they head over to the tutoring bar; if not, they open up a “playlist” of online resources for that concept and familiarize themselves with the topic using online tools before heading to the seminar later in the period. The students rotate between computer practice, seminars and individualized instruction for a two-hour math period.

Once a student has mastered a concept, she takes a computerized assessment that gauges her level of competency. But that computer score is not what defines that student’s learning, according to Miller.

“Too often we have these machine readable assessments and then students think that math is picking the right multiple choice question,” Miller said. Once students have mastered a set of skills, they complete projects to demonstrate its real-world applications. For example, to show mastery of quadratics, Miller’s students designed a water fountain with a perfect water arc for people of various heights.

Rainier and Tahoma have a project coordinator in the math classroom who keeps an eye on how all the parts work together. She’s in charge of identifying the problem points and working to come up with solutions.

PROVIDING DEPTH          

Another school in Oakland, Calif., Crocker Highlands Elementary, uses math software in a different way. Students have lab time once a week when they work on the ALEKS math software. Ashley Foster teaches fourth grade and is attempting to find ways to integrate the online learning into her direct instruction in class. While there have always been differences in comprehension in the classroom, now some of her students are actually doing fifth-grade math on the computer program while they’re in fourth grade. She still teaches the fourth-grade math in class, but she’s left asking herself questions like, “How do I challenge this student” and “Does the student feel alone when they are doing this?” because they’ve zoomed ahead to the next levels on the math software.

Foster’s solution has been to send kids who have mastered a concept into the hall to do “challenge time” — in-depth word problems that inspire critical thinking. But those more difficult concepts soon became the goal for other kids in class. Soon “challenge time” became a reward for understanding the material and all the kids wanted to work on word problems. Foster found a way to allow kids to move at different paces through the material — and inspired everyone in class to move ahead.

SOFTWARE FOR REMEDIATION

Another Bay Area school uses math software for a completely different reason. At Summit Everest in Redwood City blended learning is used to close the gap between different levels of learners. The school’s population reflects its district, which covers the whole economic spectrum: 40% free and reduced lunch and a mixed-race population.

Kyle Moyer teaches AP Calculus to seniors, but some of his students aren’t ready for the course. The school’s mission is to graduate high school students who are both college ready and equipped to succeed in college once they get there. But many come into his math class at a huge skill deficit, so he uses the software to identify the holes and gaps and help fill them.

But teaching some kids basic math while others learn advanced calculus in the same room is a tough juggling act. Adjusting to the tech tools for grading and data analysis hasn’t been easy either. Moyer says he’ll start class by discussing a broad concept that all learners can understand, then he’ll break the class into groups with some kids working to catch up on the computer and others learning calculus. He then moves around and provides individual help.

Moyer says the technology has its place and it has certainly helped many struggling students catch up. But it has limitations. “A computer as of yet cannot help a student develop that deep mathematical reasoning and connecting concepts in various areas,” Moyer said.

That’s his job, but he hopes that the software will give struggling learners a more robust mathematical “arsenal.”