Sometimes we can find hidden educational gems in places we may not think to look. Recently, I came across a great set of resources that has been put out by the New York Public Media Provider, THIRTEEN. This group produced and aired a series of math projects titled Get the Math. These projects were designed to help middle and high school students relate math to areas of interest. The activities include a video segment to set-up an interesting problem along with activities and additional “challenges” related to the video.
Each of the three projects is based on a topic that is of interest to young students:
- Math in Music – Depicts musicians using proportional reasoning to produce a song.
- Math in Fashion – Shows how a designer uses Algebra to get the production price of a clothing item within a certain range.
- Math in Video Games – Explores the use of graphs and equations to create the movement of objects in a video game.
After watching a short video, students are presented with a challenge. The program guides students to complete the challenge and then presents additional problems that are similar so that students can practice their skills. The site also includes teacher lesson plans so that participating teachers have a clear path to follow when presenting the activities.
Students are in constant need of fun, motivational activities that show them how the math they are learning may be used outside the classroom. Presenting three different contexts for activities that are engaging, interactive, and purposeful can help students recognize that many of their future careers may utilize math skills. You may even want to have your students come up with their own challenge by taping an introductory segment and developing activities much like those presented on this site. Then, have students present their work to the class so that everyone has exposure to the creative ways in which math can be used.
In a recent post, I wrote about resources that can be used to help keep students’ minds sharp throughout the summer months. Use of these sites, however, is left up to the discretion of the students or parents, and many choose not to fill their summer months with math activities. Some districts opt not to give their students a choice, and they distribute work packets that students must complete during the summer months. In my district, all students entering Grades 5 through 8 are assigned a packet in June that is due at the start of school in September.
The purpose of our math packet is to help students maintain the skills acquired in the previous year so that they have a better start in September. The packet consists of roughly 50 questions based on content that should have been mastered in previous years. The topics covered are ones that are essential for success in subsequent years. Ideally, students would complete the packet gradually throughout the summer. However, realistically we can expect that most students are likely to complete the packet at the very end of the summer...right before the start of school. By this point, students may be struggling to remember skills from the previous year. To combat this problem, our packet includes a very brief explanation on topics that are covered. For example, a particular page may include an explanation and a sample problem showing how to multiply decimal numbers followed by 8 or 10 problems on the topic. Students who are struggling can refer to the mini-lesson, and it might even assist parents who are helping their child with the packet.
I do believe that summers are meant for having fun and relaxing. However, it’s unfortunate when kids come back to school in September completely “cold”. It’s as if they haven’t thought about school at all since exiting the classroom in the spring. Requiring students to complete a small assignment over the summer, even if it is done the night before school starts, ensures that students start the school year with at least some recent exposure to math skills which will, hopefully, lead to a more successful year.
A Nobel Laureate in physics, Carl Wieman, is heading up a $12 million initiative to improve instruction with research-backed methods. A finding from his team released in the journal Science this month suggests that a "deliberate practice" lecture style could boost student learning. Such a class actively engages students and allows them time to synthesize and respond to new information.
In the study, one undergraduate physics class was lectured in its normal routine while another integrated the following elements:
- Pre-class reading assignments (three or four pages)
- Pre-class reading quizzes (true/false quizzes based on readings)
- In-class clicker questions with student-student discussion
- Small-group active learning tasks
- Targeted in-class instructor feedback
Though these techniques have been studied independently or in smaller clusters, Wieman and his colleagues combined them all in every 50-minute class. Both courses were taught as usual for the first 11 weeks, and the new style was introduced during the three lectures in week 12. Students taught in the "deliberate practice" style scored an average of 74 percent on a post-test, which was more than twice as high as the average for the comparison course.
Though promising, this study has limitations that others have pointed out. James Stigler, a UCLA psychology professor, said that it was not a good idea for the authors of the study to also be delivering the intervention. As reported by the New York Times, he explained that, "This is not a good idea, since they know exactly what the hypotheses are that guide the study, and, more importantly, exactly what the measures are that will be used to evaluate the effects. They might, therefore, be tailoring their instruction to the assessment — i.e., teaching to the test."
Have you tried those "deliberate practice" techniques before? Did you experience classroom change?
On the internet, there are tons of free materials. All one needs to do is open up Google and type in their search parameters to get pages and pages of hits. With all this information, how do we know what’s valid or not?
Fortunately, there are trusted sites out there. Below you’ll find a few of my favorite resources.
- Free Technology for Teachers: Richard Byrne highlights web resources several times a day, seven days a week. He explains what the resource is and includes application for education. Free Technology for Teachers is read by over 33,000 people daily. He covers all subjects.
- National Geographic Education: With multiple views from teacher to students, National Geographic’s education site includes photos, interactive activities, and news. The teacher section includes downloadable worksheets and multimedia activities. The site is still in beta.
- Federal Resources for Educational Excellence (FREE): One of the most popular K-12 websites, FREE offers over 1,500 teaching resources from multiple federal agencies, including photos and primary documents. This is updated frequently and covers all subjects.
The Common Core State Standards are moving toward full implementation, planned to take place in 2014. 100 schools in New York City have undertaken a trial of the new standards, which aim to standardize the nation’s curriculum and level the playing field for students across the country. So far, only a few cities have begun incorporating the standards into their schools, but educators are hopeful that the new initiative will boost academic achievement. Forty-two states as well as the District of Columbia and British Virgin Islands have adopted the State Standards.
While the Common Core provides a framework of the skills and concepts that need to be mastered at each grade level, they allow teachers some flexibility in exactly how to teach the material. The goal is to challenge students to think analytically, while raising the bar for academic achievement in many states. The Common Core endeavors to improve the nation’s quality of teaching as well. For example, in one New York math class that has adopted the Common Core, students learned about normal distributions and bell curves by plotting heights of members of their class. Through this activity, they realized that sample size is important in interpreting probabilities. Creative and engaging activities like this one teach core concepts in accessible ways.
Also check out American Educator’s Winter 2010-2011 issue, which features more thoughts on the benefit of a common core.
www.flickr.com/photos/wwworks/ // CC BY 2.0
Anyone who teaches math knows that one of the biggest challenges is dealing with students’ fear and anxiety regarding the subject. Recently, the causes of math anxiety was investigated and reported in an article published in Education Week. This article provides information about why so many people are turned off by math and why it seems acceptable for one to admit that he or she is not good at math.
First, the report states that the way in which the brain processes math problems is altered when students are anxious. Therefore, students who are stressed are less likely to perform well on mathematical tasks. This poor performance is likely to perpetuate students’ stressful feelings, creating a seemingly endless cycle of stress and poor performance. It has also been found that students with high math anxiety are likely to suffer from dyscalculia – a struggle with numerical calculations. Dyscalculia often surfaces early on as students are learning basic mathematics. Since these basic math skills are the foundation for all math, trouble early on can lead to frustration and negative feelings about math in subsequent years.
Finally, the report states that gender may also have an impact on student performance. According to the research, girls who were taught by a teacher with high math anxiety performed more poorly than boys taught by the same teacher. This implies that the attitudes of both parents and teachers do impact their students’ math performance and that girls are affected more acutely than boys. For this reason, it is so important that parents and teachers create a positive learning environment for students and attempt to disguise any math anxiety they may feel. If providing students with a low-stress, positive learning experience can improve student performance, then parents and teachers have a right to support children by doing so.
One of the challenges of teaching is presenting concepts in a clear way so students can follow and understand. But new studies show that sometimes confusion and ambiguity actually facilitate better mastery of material. A study by professors at Princeton University demonstrated that students who learned material that was presented to them in a hard-to-read font, like Monotype Corsiva, later performed better on tests than students who learned the material in a clear font, like Calibri. People seem to process information better when they have to struggle to read or understand it.
Making material more difficult to understand forces students to focus harder and to absorb the information better. It seems that making the learning process more difficult can lead to greater benefit in the long run. In a recent article for Miller-McCune, Nate Kornell, a professor at Williams College, cites more studies that reveal that harder test questions are more effective in cementing learning. If you have to work through an unfamiliar problem, you will be more likely to remember the material long-term. Similarly, by spacing out study sessions, you forget some of the material so you have to make a greater effort to recall it. This effort corresponds with mastery and understanding.
These findings are very relevant to math learning, especially math fact fluency. According to Kornell, “we know that if you study something twice, in spaced sessions, it’s harder to process the material the second time, and people think it’s counterproductive. But the opposite is true: You learn more, even though it feels harder. Fluency is playing a trick on judgment.” Perceptual fluency and retrieval fluency are not necessarily equivalent. Mastering math facts involves developing retrieval fluency. Making students think hard to learn facts in spaced study sessions may allow retrieval to come more easily.
For more interesting thoughts on the science of psychology and learning, check out Miller-McCune’s Think Again blog.
This time of year, parents are asking me what they can do to help their children maintain skills over the summer. While most parents do not want to subject their kids to hour after hour of math drills during their break, many do want their students to continue to practice their skills throughout the summer months. We all know that math is all around us, but parents often have to make math more explicit to ensure their students recognize how they use math outside the classroom. Depending on the student’s level, parents can play counting games with kids, look for shapes in nature, or help children work with money during a vacation.
Recently, I came across this website from Education World that provides several ideas to help students engage with math activities throughout the summer. This site provides a plethora of activities arranged in several categories:
- Planting a Math Garden: Includes activities to help students see how math is used in their every day lives.
- Math Bedtime Stories: Read these mathematical tales to your little ones!
- Math and Sports: Browse through several links to help students see how math is embedded in sports.
- Math in Games: Kids love playing games, so it’s great to use game time to practice math skills.
- Math and TV: Make their TV watching worthwhile by including fun math-related activities.
- Math + Computers = A Great Equation: On those rainy days, provide kids with this list of links which include games and activities to help them practice their math skills.
- Math at Home, around Town, and in Nature: Don’t leave the house without helping kids see how math is all around us.
- Shopping: Especially suited for older students, estimation and money-related activities are easy to incorporate while shopping.
- Math Travels: Utilize spare time during trips to help students see how math is used when planning and paying for a vacation.
- Eating, Sleeping, and Growing: These extra activities may fill up other spare time kids have during the summer!
Summer break is a time for kids to relax and have fun. I don’t believe that students should spend all of this time crunching numbers. However, as this site shows, there are plenty of opportunities to help students appreciate math and have a little fun while they’re doing it!
The school year is winding down, standardized tests are coming to an end, and we’re starting to tie up loose ends before leaving school for the summer. Many of my colleagues are using the last weeks of school to cover topics that weren’t taught prior to the state tests. However, many teachers are also fitting in some low-key learning days to give students a break and show them that math isn’t just about crunching numbers. For some, these fun-filled days may include a movie-showing where the feature film highlights an aspect of math.
Websites such as Mathematics in Movies, provide information about math references in movies. Many of the references are minor and many of the movies may not be appropriate for your audience. However, there are several movies that are math-related and may inspire your students and provide a context for the math topics they have been studying. Some of my favorites include:
- Stand and Deliver (Rated PG): In this movie, appropriate for middle- and high-school students, an inspiring teacher motivates students to learn Calculus and helps them recognize their potential.
- Donald in Mathmagic Land: Elementary or middle-school students will enjoy this animated feature in which Donald Duck shows how math can be used in everyday life.
- Contact (Rated PG): Characters in this movie use math, specifically prime numbers, to communicate with an alien civilization.
If you’re interested in having your students follow along with worksheets during the movies, find a site like MathBits which includes a plethora of resources. Be sure to review the resources prior to using them as some of them may be far advanced for your students. If you’re motivated, you could make your own worksheets to ensure that they are age-appropriate. So, go ahead, have a little fun this spring. Your students are likely to get excited about watching a film in class, and if it helps them appreciate math, then it’s well worth it!
A few weeks ago, we wrote about the Museum of Mathematics
opening in Fall 2012.
If that feels like too far away, there's good news! The executives of the upcoming math museum have been testing the water for the past two years with a traveling math exhibit called Math Midway, and it's still making its way from coast to coast.
Here are some of my favorite exhibit activities:
- Pedaling on a squared-wheel tricycle: Students learn about how math can help with figuring out how to shape the bumps on the road to make the wheels roll smoothly.
- Balance a pirate ship: Visitors use math to balance the weights on both sides of the ship. On each side, there are three posts, spaced at equal intervals, from which the participant can hang weights. A weight on post 2 has twice the effect of one on post 1, and a weight on post 3 has 3 times the effect. Participants can choose from brass rings of varying weights to balance the ship.
- Mirror morph: Children can control their reflections by pulling on a handle to change the curvatures of mirrors to learn about how light affects convex and concave surfaces.
Currently in Dallas, the math exhibit is scheduled to travel to New York, California, New Jersey, Ohio, Maryland, and Florida.
If you could design an exhibit for the future museum, what would it be? Have you seen any good math exhibits in the past?
Photo credit: mathmidway.org/math-midway-activities-pedal.php
The popularity of LOL Cats is a universal fact. We see this particular meme across the internet, including Facebook and Twitter.
While it has reached viral status, the sister site Graph Jam has not. Graph Jam is a meme-based website that allows users to create their own content. You can create pie charts, bar graphs, line graphs, Venn diagrams, or equations. Of course, a lot of the ones already created border on silly, but the graph generator can still be used to create graphs and diagrams that relate to the day's hot topics, while developing a better grasp of what the structure of a graph means.
Since Graph Jam doesn’t deal with actual statistics, numbers are not relevant (remember, this site is designed for laughs). The site is ideal for creating charts for the students to figure out percentages or relationships.
The downsides to this as an educational tool are that it limits you to saving the graphs on their public site, and printing is problematic at best. Nevertheless, at its core it gives students an amusing opportunity to better understand different types of chart creation.
Photo credit: cheezburger.com/FlashBuilder/GraphJam
Many times, if you walk into my room when I am working with my 5th grade students, you’ll notice that several of them are sitting on their hands. No, this is not because they are disturbing one another but, instead, it is to prevent those students from using their fingers to compute. When fellow teachers walk in, I sometimes get applauded for my efforts, but more often than not, teachers question my tactics. If it helps them get the correct answer, then why does it matter? It matters because, in my opinion, anyone beyond the age of 7 or 8 doesn’t need to use their fingers when doing calculations that could be done in their head.
It is true that one’s fingers can be used to successfully arrive that the correct sum, difference, or product to simpler problems, but the issue I have with this method is that students become far too reliant on their fingers. You see, when we’re first introducing computation in the early elementary grades, counting and computing with fingers may make sense because students are in the concrete learning phase. Fingers are a handy manipulative that young learners always have with them. The problem is that this “finger computing” habit is one that is very hard to break and may prevent students from moving from the concrete to abstract learning phase. Sure, some students will naturally move away from using their fingers as they begin to master facts. But there are some students who will never see a reason to internalize their facts because they always have their fingers available to them. There comes a time, however, when using fingers is inappropriate for most students. For me, that time is in the fifth grade…if not earlier.
Yes, students will “discover” their fingers and recognize that they can use them to complete some simple tasks, and that’s fine. My suggestion is not to promote the use of fingers for computation. Instead, suggest the use of external manipulatives such as counters. If a student has to get up and get counters each time he wants to compute, he’s likely to be more motivated to learn the facts. Inspire your students to see the math through the use of manipulatives, but also help them find success with abstract mathematical ideas.
Recently, I have noticed that the middle school students I tutor, when faced with a tough arithmetic problem, don’t immediately reach for paper and pencil. My automatic strategy when I have to multiply two two-digit numbers is to do the calculation out by hand. These kids, though, start thinking aloud and break down the problem into its component parts.
36 x 54: They recognize that 30 x 50 is 1500. Then 30 x 4 equals 120. 50 x 6 is 300, and finally, 6 x 4 equals 24. Adding 1500 + 120 + 300 + 24 yields the correct answer, which is 1944.
These days, the emphasis in learning arithmetic is no longer on the rote calculations. It’s true that long division and multiplication have become somewhat obsolete in an age of technology. People in their real lives do not have to solve difficult problems by hand. Instead, they can plug them into a calculator or spreadsheet and the calculation is performed for them.
However, students still need to develop strong algebraic thinking skills, and arithmetic is the gateway to algebra. After all, arithmetic is useless unless you know what calculations you need to enter into the calculator or computer. The Math Guy at NPR, Keith Devlin explains in a March segment that the important skill to develop these days is an understanding of the number system and what numbers mean. Therefore, using this new strategy for multiplication, the students go through the process of identifying each of the smaller multiplication problems within the larger one. They are able to practice their multiplication tables while making sense of how they are arriving at the answer to the question: what is 36 x 54? Elementary and middle school math these days utilizes a totally new approach to the subject than the one I learned in school. But this new approach is just another example of how education is adapting itself for the 21st century.
As a math lover, I rarely need a special reason to do math problems. However, some students might need a bit of extrinsic motivation to help them along. St. Jude’s Math-a-thon might just be the perfect activity to inspire kids to solve lots of math problems while fundraising towards a great cause. The Math-a-Thon is a free program that is appropriate for students in grades K–8 and benefits St. Jude Children’s Research Hospital. This cancer research center treats hundreds of children each day, regardless of whether their parents are able to pay for their medical care. The daily operating cost of the facility is $1.5 million, most of which is covered by public contributions.
The program was first designed to supplement the curriculum while teaching children the importance of helping others. Students who chose to participate ask family and friends for pledges to solve math problems in the Math-a-Thon Funbook. The Funbook is created by Scholastic and includes grade-level problems designed to align with the curriculum and prepare students for standardized tests. Upon completion of their Funbook, students collect donations from their sponsors and the money is sent directly to St. Jude’s Children’s Research Hospital. Beyond the benefit of increasing math comprehension and helping a good cause, students and schools can earn prizes depending on amount of money collected.
Children tend to be eager to help those around them and this activity seems like the perfect opportunity to persuade kids to compute while benefitting their peers. It may be too late to plan a Math-a-Thon for this school year, but it’s the perfect time to start thinking about an event for the next school year. The website has a plethora of information and provides tips and tools for teachers, students, and parents to get kids started on solving for a good cause!
Photo credit: www.mathathon.org/index.shtml