Math Field Trips & the Musuem of Mathematics

  

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This time of year, it seems that school field trips are occurring almost every day. Most of them are visits to museums or other exhibits sponsored by Science, English or Social Studies departments. For obvious reasons, students look forward to these trips and often favor those classes because of these fun activities. It’s rare that an opportunity arises to take a math field trip, but fortunately, that is all about to change. In the Fall of 2012, the Museum of Mathematics, known as Mo-Math, is scheduled to open in New York City.

The concept of the museum came about after the closing of a smaller math museum in the area. The museum’s board recognized that there is no other museum of mathematics in the country despite the fact that plenty of dynamic exhibits are possible. The group feels the need to improve the public perception of mathematics and this will require a cultural shift. In general, people need more exposure to math, and this museum will do just that. Specific goals of the museum include:

• A Mathematical art gallery showcasing changing exhibits that explore the relationship between math and art.

• Activities that highlight the role of mathematics in our society and reveal the connections between math and music, math and literature, and math and finance.
• Additional innovative and exciting exhibits where visitors can experience a hands-on sense of wonder and discovery.

Recently, the museum received a $2 million grant from Google and is close to its fundraising goal. Some exhibits, such as The Ring of Fire, are already traveling to museums throughout the country. In addition, the museum has already begun presenting monthly lectures related to math.

According to Cindy Lawrence, the museum’s chief of operations: "We're on a mission to change the way folks think about mathematics and their perception about mathematics. America is pretty low in mathematics proficiency and we're trying to change that." While not everyone will be able to take a quick field trip to this institution, many will be able to take advantage of its traveling exhibits. Let’s just hope that this will be the first of many such museums throughout the country.

Stories in Education: How Do We Learn?

  

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In a contribution to the ongoing discussion of the best ways to facilitate learning, Sam Chaltain, along with other educators, has launched the website Faces of Learning. An offshoot of his book, also called Faces of Learning, the website allows people of all ages to share their most powerful learning experiences. These stories are posted for everyone to read and appreciate. The new Faces of Learning website is part of a larger campaign that includes an “engagement tour” with events centered around people sharing their learning stories, a weekly radio series, and weekly stories posted in the Washington Post.

The recently released book includes 50 inspiring stories about learning that Chaltain compiled from important political figures such as Secretary of Education Arne Duncan and Senator Al Franken, as well as many artists, teachers and others. Chaltain was the national director of the Forum for Education & Democracy, an education advocacy organization, and the founding director of the Five Freedoms Project, which helps educators create democratic learning communities.

The website also offers other exciting resources for both students and teachers. Visitors can take a quiz that determines their strengths and weaknesses as a learner. And Faces of Learning provides a list of ideas on how to create more ideal learning environments, with helpful links for educators and parents. For example, here is a partial list for how teachers can be resourceful:
 

Get Resourceful

• Equip Your Toolbox with Q.E.D.
• Institute Morning Meetings
• Imagine New Designs for Learning
• Track the Aspirations of Your Students
• Experiment with Open Space Technology

View the rest of the Faces of Learning resources.

http://www.flickr.com/photos/chicago2016/ / CC BY 2.0

Earth Day 2011: What Is Your Water Footprint?

  

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We celebrated Earth Day on April 22^nd, but you don’t need me to tell you we should be aware of our impact on the environment every day.

One way to do this is with National Geographic’s Water Footprint Calculator. The calculator asks you various questions about your lifestyle and uses various mathematical formulas in the background to let you know where you fall on the water usage scale.
 

Application for Mathematics:

Split the class into separate groups. Each group should have two sets of information, either their own or prepared information, to enter into the calculator. Have them record their first set of results and repeat the activity. Once the second round is complete, have them discuss what factors impacted their water footprint the most. What is the significance of the water-usage numbers in their own lifestyles?

Read more about how the Water Footprint Calculator works.

Our Nation's Debt: How Much Is 14,000,000,000,000?

  

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Not a day passes that I don’t turn on the news and hear something about our country’s financial situation. Lately, the focus has been on the so-called debt ceiling which doesn’t seem much like a ceiling to me. Instead, it is an arbitrary number that our debt shall not exceed at any given moment. However, it seems that our debt just keeps getting bigger and bigger and few people seem affected by it on a day-to-day basis. What’s most concerning is that our students, those who will be facing the debt in upcoming years, probably understand very little about the magnitude of our debt. This is because there are few numerical situations that can compare to the number that represents the amount of money our country owes.

Let’s change that…let’s start doing more to educate our students about this enormous problem with the hope that, through understanding, students will better be able to tackle this challenge in the future. Our published national debt is roughly $14 trillion. What does this mean to middle school students? It probably doesn’t register beyond knowing that trillion is one thousand times greater than billion; but again that doesn’t mean much when they don’t have an understanding of how much a billion represents. Students need help with understanding just how much money we’re talking about. Life’s Little Mysteries has created an infographic that depicts the size of our national debt in pictures. Have your students take a look at this infographic...it does help to put things into perspective just a bit. Perhaps you can even have your students develop their own infographic to depict the size of our debt. What a great visual and collaborative activity for students!

Helping students see how great our country’s debt is will not eliminate the debt. However, it will help our students grow to be informed, knowledgeable citizens. Remember, our debt isn’t going to disappear in the next 5 to 10 years, so these students wil be our future problem-solvers to help alleviate some of this pressure. What better way to prepare them for such a grand task than to begin educating them about where our nation stands?

What Can We Do to Encourage Student Curiosity in Math?

  

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San Diego math teacher Osvaldo Soto has set out to address why so many students struggle in math at the middle and high school levels, according to an article in the San Diego Union-Tribune. Even students who excel in elementary school may later fall behind, lacking the necessary foundations to move on to Algebra, Geometry, and upper-level math. Soto believes that teachers are too quick to show their students short cuts to solve problems. These tricks and shortcuts may be effective in the short run, but students fail to develop the analytical skills to solve the problems on their own. And too often, they don’t even understand how they came to the answer.

While tutoring middle school students in math recently, I have noticed that many of them try to rush to get to the answer without really understanding what the problem is asking. When I ask them to show and explain their steps, many times they are unable to justify what they are doing. One student was trying to plug numbers into the Pythagorean Theorem but did not know the definition of the hypotenuse. This student clearly had some critical gaps in his knowledge of geometry. He was trying to plug numbers into a formula he had memorized, but he had not mastered the essence of the concept.

While adults who are more familiar with math may rely on quick shortcuts, it is important for students to employ analytical and quantitative thinking skills when approaching problems. These skills will help build the foundations for success in math. Soto, a member of Math for America San Diego, is trying to revive math instruction by encouraging students to think and to be curious about math.

What are some strategies you use to develop students’ conceptual understanding? And how do you promote curiosity in the math classroom?

Visualizing 3-Dimensional Images with One-Point Perspective

  

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You probably have noticed that when you look at an illustration of a cube, the parallel lines are on an angle. This is called perspective.

There are multiple types of perspective: zero-point all the way through four-point perspective. The most popular one is one point perspective. This is where all parallel lines converge on one central point.

One point perspective drawings are a fun way to create simple three-dimensional drawings and show how parallel lines are used in everyday life. Here you can watch a video that explains the key concepts of one-point perspective drawing:

To help students draw 3-D pictures themselves, here are several worksheets dealing with one-point perspective.

Teacher Collaboration: Sharing Ideas to Improve Instruction Together

  

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When I first began teaching, I put a lot of effort into each of my lessons. I would spend hours writing plans and creating worksheets. In my immaturity, I rarely shared my lesson ideas with colleagues because I felt that, if I was the one who put all of the effort into the lesson, no one else should reap the rewards of teaching that lesson. In turn, I rarely asked others for lesson ideas or suggested collaborating to develop lessons. Twelve years later, my perspective has completely changed. Now, I see the tremendous value in collaboration and lesson sharing and am working with my district to ensure teachers are involved in these practices.

In order to facilitate collaboration, our district has provided teachers with common planning time which allows teachers in similar content areas to work collaboratively on lessons and activities. Initially, this was challenging because teachers wanted to use the time to work on their own tasks. However, with a bit of guidance, teachers have discovered how to really utilize this time. The math teachers work on grade-level lessons three days per week; one day is focused on differentiated instruction activities; the fifth day is a group discussion about how everything is going. Using this method, teachers aren’t working in a “silo” to create all of their own lessons like I once did. Instead, they are discussing how they can develop lessons that will benefit all of their students. As an added bonus, the teachers have learned that some stress is alleviated when they can “divide and conquer” some lessons that are more time-consuming to develop.

We’re still working on the best ways to share lessons more easily. Fortunately, there are several tools on the internet that allow you to do this. File sharing websites such as Google Docs and Wiki-Teacher allow teachers to share content with those within their school and others outside their districts. Some sites allow schools to develop their own internal sharing site so teachers can easily upload the documents they have created collaboratively. Why not look at some of these sites for lessons created by teachers all over the country? No need to reinvent the wheel! Don’t make the same mistake I did early on...remember that, as teachers, we are all in this together. Use common resources to give your students the most diverse experiences possible.

Quantile® Teacher Assistant Supports Differentiated Math Instruction

  

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Our friends at MetaMetrics, who last month gave us an article on Quantile^® Knowledge Clusters, here describe the value of the Quantile Teacher Assistant in planning out math instruction.

The Quantile^® Teacher Assistant utilizes The Quantile Framework for Mathematics to provide teachers with a practical tool for differentiating mathematics instruction. The Quantile Teacher Assistant has information about the QTaxons associated with teachers’ own state standards. More than 23 state standards and the Common Core State Standards have been aligned with the Quantile Framework, and new states are added each month. Teachers can use their state standards to access the knowledge clusters and the free resources that are associated with each skill. 

With the Quantile Teacher Assistant, teachers first identify the state, grade and standard they plan to teach. Based on this information, a three-tiered page of the QTaxons related to that standard is presented, with the focus QTaxon(s) listed in the middle column. Surrounding the focus QTaxon(s) are prerequisite QTaxons in the left column, supplemental QTaxons below the focus QTaxon(s), and impending QTaxons in the right column:

• The focus QTaxon(s) describes measurable skills connected with the chosen standard that are in the learning frontier of a student. The student is prepared for instruction in the skills associated with the focus QTaxon(s).
• Prerequisite QTaxons represent skills that must be learned before the student can fully understand the focus QTaxon skills. Prerequisite QTaxons can be used to identify extra support for students who are not at the level of the focus QTaxon(s).
• Supplemental QTaxons describe topics that will support or enrich the skills associated with the focus QTaxon(s).
• Impending QTaxons represent skills that extend beyond the focus QTaxon(s) and can be used to provide a challenge and breadth to students who have already received instruction and experienced success with the focus QTaxon(s). 

By clicking on “(More)” after each QTaxon description, a teacher can access additional teaching resources for each QTaxon, such as activities and worksheets, web-based games and instructional videos, and key vocabulary words.

An additional feature of the Quantile Teacher Assistant is the ability to use the Quantile measures of students in a class to identify their likely success with an identified set of QTaxons. On the QTaxon display directly above the focus QTaxon is a bar with two sliders. The sliders can be moved to the left or right to capture the range of students’ Quantile measures. This range determines the color of the QTaxon boxes. Yellow/orange boxes identify the QTaxons that are within the range of the students’ Quantile measures. Green boxes identify the QTaxons that represent the skills that are below the students’ Quantile range and describe skills they can likely use in problem-solving situations. Red boxes identify the QTaxons that are above the Quantile measures of the students’ ability levels. These skills will be great enrichment to challenge the learners who can move forward through instruction quickly. 

The Quantile Teacher Assistant takes the guesswork out of differentiating instruction in today’s diverse mathematics classrooms. By using the Quantile Teacher Assistant, teachers no longer need to search the internet for resources to ensure they reach all learners. The Quantile Teacher Assistant provides teachers with multi-leveled assistance for teaching the entire math curriculum with numerous resources that include lesson plans, worksheets, video tutorials, demonstration tools and worksheets.

Photo credit: http://qta.quantiles.com

Are Kids in Korea Spending Too Much Time on Math?

  

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Officials in South Korea are tracking down "cram schools" that go past their 10 p.m. curfew and have students in uniforms working on math problems deep into the night. The Education Ministry even offers rewards to tipsters. The Washington Post reported that more than three quarters of students in Korea enroll in private tutoring, the highest rate in the world. More than $19 billion was spent on private tutoring in 2009, more than half the amount spent on public education.

Some wonder if Korea's impressive statistics in education come at too high of a cost. Korea regularly ranks near the top in international math exams, such as the PISA. Their high school dropout rate is less than four percent. College completion is at 56 percent, among the highest in the world.

However, Korea's Minister of Education, Lee Ju Ho, expressed his concern to the Post that much energy "has been spent on raising test scores, not nurturing creativity or any other aspect of human nature." This sentiment jibes with conversations that I've had with colleagues who say many families in other countries want their kids to do their primary and secondary schooling in the states to develop into more well-rounded individuals with talents outside of academics and that have social lives.

If the international exams tested creativity and other 21st century skills, do you think the U.S. would be at the top of that ranking?

www.flickr.com/photos/knittymarie/ / CC BY 2.0

Helping Students to Want to Be Good at Math

  

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Most educators, especially math teachers, are passionate about mathematics. However, not all students have the same respect for the subject. Cossondra George recently published an article in Education Week providing tips about how to build students’ aptitude and engagement with mathematics. “While it is considered unacceptable for the average person to lack basic reading and writing skills,” she writes, "people often brag about their inability to ‘do math.’ It is almost a badge of honor to be numerically challenged.” Here, George highlights the reality that society often believes it is acceptable not to be good at math. 

In her article, George provides six suggestions to increase students’ level of confidence with mathematics.

• Purchase a set of whiteboards for your class – These help students engage with the lesson and practice concepts with their easy-to-erase tools. Even reluctant students can have fun solving problems on the whiteboards.
• Create real-life examples of concepts you are learning – Go beyond story problems offered in textbooks and create problems that relate directly to students’ lives.
• Teach the power of “Is your answer logical?” – Students need to understand that math isn’t just about a process but also about a logical solution. Always require that your students look back at the original problem to be sure their solutions make sense.
• Integrate technology to capture student interest – Students live in a technological world, so bring that world into the classroom through interactive games and activities.
• Encourage, require, and demand re-dos – By correcting missed problems, students identify their mistakes and take pride in working through the correct solution.
• Use small groups and presentations where students teach each other – Students learn better when they teach a topic and other students are likely to be highly engaged when learning from their peers.

Each of these suggestions will help improve the disposition of your students. Try some of these suggestions to make your classroom one where the inability to do math isn’t acceptable, and instead, students are urged to be true mathematical thinkers.

Free Resources: What Are Good Questions?

  

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A teacher’s best tools to stimulate math discourse are Good Questions. A Good Question is an open question, where there may not be a right answer. Instead of returning a memorized fact, students must think critically and reason out their understanding of a concept. Good Questions are common in classes like Social Studies, where students are often encouraged to form opinions and defend their ideas. But how do a Good Questions fit into math class?

Just as it is with social studies, these good, open questions are invaluable to a skilled math teacher. Careful, intentional and mindful questioning helps students not only retain new knowledge, but understand it too. So what do good questions in math look like?

• They help students make sense of the mathematics.
• They are open-ended, whether in answer or approach.
• There may be multiple answers or multiple approaches
• They empower students to unravel their misconceptions.
• They not only require the application of facts and procedures, but encourage students to make connections and generalizations.
• They are accessible to all students in their language and offer an entry point for all students.
• Their answers lead students to wonder more about a topic and to perhaps construct new questions themselves as they investigate this newly found interest.

View these helpful resources to explore how to use Good Questions in your classroom and implement them into your lesson plans:

The Importance of Questioning
What Are Good Questions?
The Practice of Good Questioning
How Are Good Questions Created?

Grades K-6 Lessons:

What Could Be the Sum? A Lesson with Third Graders

Grades 5-8 Lessons:

Number Relationships: A Lesson for Fifth through Eighth Graders
Using Questions in Math Lessons: Ideas for Grades 5-8
 

To learn more about Good Questions and find even more resources, visit the Math Solutions – Math Talk page.

Generating Math Talk That Supports Math Learning

  

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Here's an excerpt from an article by Lisa Ann de Garcia of Math Solutions that illustrates how to get students talking in math class. To read the full article, please follow the link at the bottom.

Due to the attention in the last few years on discourse and its importance to student learning, educators nationwide are finding that they can help children become confident problem solvers by focusing on getting them to talk and communicate in partnerships, small groups, whole groups, and in writing. In addition, English Language Learners are flourishing as they experience focused opportunities for talking and trying on new mathematical vocabulary.

So what exactly is discourse? What are the teaching practices associated with successfully establishing an environment to support it, and as a result, to improve mathematical proficiency? How does one begin to elicit meaningful talk during math lessons? As a profession, we share a vision about the role student discourse has in the development of students’ mathematical understanding, but are often slow to bring the students along. Children do not naturally engage in this level of talk.

This article addresses the above questions and concerns—and more. It opens with a look at discourse through NCTM’s definition and its involvement with the Common Core State Standards. It then focuses on literature available on discourse, specifically the book Classroom Discussions, and addresses five teaching practices focused on the how to of getting students talking about mathematics. The article concludes with journaling insights on discourse from a kindergarten and second-grade classroom. This article is by no means an exhaustive list of discourse “to dos;” hopefully it will however get us all started in thinking about and implementing best talk practices.

Read the full article to explore the 5 teaching practices to get students talking about math.
 

To learn more about Math Talk and find resources for implementing these practices in your classroom, visit the Math Solutions – Math Talk website.

'The Chess Lady' Brings Chess to Classroom Learning

  

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Chess has been gaining momentum in the classroom, and not just as an afterschool activity. The First Move program, developed by America’s Foundation for Chess, teaches second and third grade students the game of chess as part of their curriculum. Wendi Fischer, known affectionately as “the Chess Lady,” visits classrooms around the country to promote chess as a learning tool that teaches quantitative, reasoning and spatial skills. The program, recently featured in USA Today, aligns to state standards and is used in more than 2,000 classrooms across the country. Students enthusiastically embrace the opportunity to incorporate a game into the classroom. And who doesn’t love fun learning?

For second and third graders, developing critical thinking and problem-solving skills through chess helps them be more successful later on in algebra. The gridded board introduces students to the concept of coordinates and, consequently, graphs. Students must visualize how the pieces can move around and make sense of the rank and file system for plotting coordinates (ranks are horizontal rows and files are the vertical rows). Other subjects get a boost from chess as well. As an international game with such a rich history, chess presents an opportunity to teach about the Middle Ages. In fact, the Chess Lady visits classrooms attired in medieval garb.

It’s no wonder that students are excited about chess. And studies have shown that students who learn chess showed higher levels of academic achievement. This achievement may be attributable to improved reasoning and problem-solving skills, but it also probably reflects students’ desire to perform well when they think of learning as fun. As Fischer points out in an article for New Horizons for Learning, chess is associated with being smart. And if being smart becomes cool at an early age, students will inevitably perform better in school. 

Math Activities: The Numbers of Major League Baseball

  

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Last weekend marks one of my favorite times of the year – the opening games for Major League Baseball. I always find the winter months to be a bit boring because I can’t watch my favorite team, the New York Yankees, play ball each evening. Of course, you can imagine that there’s more to the baseball season than just balls and strikes. Like so many things that I am passionate about, I always look for the math in baseball. Finding mathematical connections to students’ interests will lead to more successful lessons and more motivated students. There are so many possible math activities using baseball statistics, but it’s up to you to be sure the math involved is appropriate for each student’s ability level.

My favorite lessons dealing with baseball and mathematics are those that help students understand decimals. One of the most common uses of decimals in the “real world” is in describing baseball batting averages. We see numbers like .305 or .240, but do the majority of baseball fans know what these numbers really mean? It’s a great topic to delve into, because it will help the students better understand the game and what a batter has to do to improve his average. At the same time, it will help students understand the value of decimal numbers. While the batting average is the most familiar statistic that uses decimals, similar studies can be completed using a batter’s on-base or slugging percentage. Another great activity is to help students determine a team’s winning percentage by dividing the number of wins by total games played. It might even be fun to have a student track a player's or team's statistics for an extended period of time.

If you take one look at the Major League Baseball site, you will see a plethora of statistics that students are able to work with. And because teams play almost every night, the statistics change daily, so there’s never a shortage of math to be completed! So go ahead, take baseball from the field into the classroom. I’m sure that your students will have a ball!

Math Is Poetry; Poetry Is Math

  

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April is National Poetry Month, and if you want some literary inspiration, head over to the on-going collaborative effort http://mathpoetry.wikispaces.com/.

I suppose what I love about these poems is that the passion of these mathematicians for their field comes through loud and clear. Happy Poetry Month!

A Mathematician's Nightmare, by JoAnne Growney

Suppose a general store --
items with unknown values
and arbitrary prices,
rounded for ease to
whole-dollar amounts.
Each day Madame X,
keeper of the emporium,
raises or lowers each price --
exceptional bargains
and anti-bargains.
Even-numbered prices
divide by two,
while odd ones climb
by half themselves --
then half a dollar more
to keep the numbers whole.
Today I pause before
a handsome beveled mirror
priced at twenty-seven dollars.
Shall I buy or wait
for fifty-nine days
until the price is lower?
 

A note from Ms. Growney: The price-changing scheme of this poem is derived from a version of the Collatz Conjecture, an unsolved problem that has stolen hours of sleep from many mathematicians. Start with any positive integer: if it is even, take half of it; if it is odd, increase it by half and round up to the next whole number. Collatz' Conjecture asserts that, regardless of the starting number, iteration of this decrease-by-half-increase-by-half process eventually leads to the number one.

And another, from a book review by Gaurav Bhatnagar:

Beauty in mathematics,
said Polya,
is seeing the truth
without effort.

Everything
in The Book
is as elegant,
as could be.

Everything
as simple,
as effortless,
as should be.

Everything
as beautiful,
as it is.

Math, Careers, and the Best Jobs of 2011

  

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When dealing with elementary and middle-school students, it’s often difficult to help them see further into the future than the next weekend. However, students at this young age should be setting long-term goals and begin thinking about potential career options. While we all know that their plans are likely to change many times before they head out into the work force, it is beneficial for them to at least come up with a few options. This will allow them to set the short-term goals necessary to head in the right direction, and in many cases it will give more meaning to what they are learning in school.

Recently, CareerCast.com published the Top Best Jobs of 2011 based on work environment, stress, physical demand, and hiring outlook. The top spot was secured by Software Engineer, but the number two spot is Mathematician, the number three spot is Actuary, and the number four spot is Statistician. Based on this information, it seems that being a motivated, hard-working math student in the early grades can lead to more than just a good grade on a report card. Students who master elementary math content are likely to do better in higher-level math courses. These courses are the ones that are necessary to secure our nation’s top jobs. 

The challenge for teachers is getting students to look into their future and think about potential careers. It’s especially difficult to get them to understand jobs such as “mathematician” and “actuary” because these aren’t careers that they are likely to be familiar with. Start hosting a math career day to help students learn about such jobs, as well as to gather more information about how math is used in more familiar jobs like an accountant or engineer. They may have to do a bit of research, but it’s a great opportunity to help kids make connections, write in math class, and perhaps even stumble upon a future career.