We can all remember times when we doodled in class. Vi Hart has taken this artistic outlet and added a math twist. Hart, who calls herself a “mathemusician”, has created a series of YouTube videos that simplify complex mathematical concepts with visual explanations.
Check out this video by Vi Hart that turns prime numbers and Pascal’s Triangle into an exciting doodled art project. It includes several number games that can be “played” casually on scrap paper. I love watching how patterns take shape on the page as she goes.
A quirky interview with Hart can be found in a January article from the New York Times. She claims she wants to be “the ambassador of mathematics,” and with the following she has been gaining through her videos, she’s well on her way.
Get excited!! April is Math Awareness Month! This event is held each April to increase public awareness and appreciation for mathematics. This year’s theme is Unraveling Complex Systems, which studies questions such as How do epidemics spread? and How do birds flock? While this topic may be a bit complex for some of our students, celebrating Math Awareness Month gives us reason to highlight math education and, perhaps, include a few special activities in our daily lessons. Set aside 5 minutes per day to discuss a special math topic, or choose one day per week to play fun math games!
In my experience with celebrating Math Awareness Month, I’ve learned that it is really important to get over-the-top excited about the event. Now, if your students are like mine, they’ll think you’re a bit “out there” and say that you like math way too much. But even the most reluctant learner is more motivated by an excited teacher. So in the weeks leading up to April, I build the excitement by doing a daily countdown and previewing some of the activities that we’ll complete. I’ve tried a couple different methods of celebrating the month, but what has worked best for me is to introduce a daily “Math Mystery”. At the start of class each day, I assign a math question or brain teaser that each student must solve. Ideally, the activity takes 3-5 minutes to complete and can be successfully answered by all students in the class. Students solve the problems on an index card that I collect daily. The cards are returned with a smiley face (correct) or sad face (incorrect). Students track the number of questions they get correct and, at the end of the month the student(s) with the most correct answers win a prize – usually a pizza party for the student and 3 friends.
It’s also a great idea to get parents involved with the celebration. It’s the perfect time of year to have a Parent Math Night to get the community involved. Or, just suggest that your students share the daily Math Mystery with family members at home. This is likely to lead to some interesting math discussions around the dinner table. So, go ahead and have fun celebrating Math Awareness Month!
And share your ideas...what are you going to do to get our students excited?
Math should not only be taught as a real-world skill that we’ll use for the rest of our lives, but also as an illustration of its relevance to current events.
During this year’s VCTM conference, Michael Bolling, the Mathematics Coordinator for the Virginia Department of Education, said connecting math to current events was a challenge many teachers face. Bolling suggested that math teachers ought to take current events, like the recent events in Japan, and find a way to connect the events to math instruction.
With the earthquake in Japan, students can learn about the math behind the Richter scale to develop a stronger understanding of the enormity of the quake. An article from the Charlottesville Examiner observed: “Bolling began by citing the then 8.9 (since reevaluated to 9.0) magnitude of the earthquake and subsequent tsunami off the coast of Japan that happened earlier than morning. The Richter scale is based on a logarithm of base 10, meaning a 9.0 maginitude earthquake is 10 times stronger than an 8.0 quake, etc.”
As more news pours out of Japan, there will be more teaching opportunities, not just in mathematics, but in every subject. The New York Times has a nice round up of lesson ideas that they continue to update:
Teaching Ideas: The Earthquake and Tsunami in Japan
20 Ways to Teach About the Disaster in Japan Across the Curriculum
www.flickr.com/photos/gsfc/ / CC BY 2.0
As another school year nears the end, reports tend to surface about graduation rates and, subsequently, drop-out rates. I began reading an article about drop-out rates when I remembered a report I read several years ago regarding this subject. The report, Approaches to Dropout Prevention: Heeding Early Warning Signs With Appropriate Interventions, details some factors that may indicate a higher chance of student drop-out in high school and provides interventions for decreasing drop-out rates. Of particular interest to me, is the information provided about the correlation between early math success and future drop-out rates.
Among other indicators, the report states that low performance in core subjects such as math may lead to a greater likelihood of a student dropping out of high school. One study mentioned in the article indicated that "more than half of sixth graders with the following three criteria eventually left school: attend school less than 80 percent of the time; receive a low final grade from their teachers in behavior; and fail either math or English. Eighth-graders who miss five weeks of school or fail math or English have at least a 75 percent chance of dropping out of high school." While the factors expand beyond a failure in math class, the fact that students who struggle with math may be more likely to drop out of high school implies an urgent need to help students succeed in elementary and middle school mathematics.
The report includes a plethora of strategies to prevent future high-school students from dropping out. Some of these suggestions include establishing a data system that tracks individual grades and monitoring grades in core academic subjects early on. Upon identifying at-risk students, the report offers suggestions for interventions such as offering tutoring sessions, establishing learning communities, and providing opportunities for catching up on missed content.
As math educators, we recognize the importance of helping students succeed in early math classes so that they may find success in higher-level math. However, this report indicates that there is a far more important reason to ensure that all students have the support and tools for success in elementary and middle-school math. Knowing that we can help prevent students from dropping out of high-school gives me even more motivation to do all I can for my students.
Too many young students enter school with low expectations for themselves. If they have not performed well in the past, they assume that their track for the future will be continued underperformance. A recent article in the Wall Street Journal highlights a survey conducted last year by Gallup, Inc., which revealed that only 42% of students aged 10 to 18 are actively pursuing their goals. However, the article also reports that goal-setting programs implemented in Texas and Virginia schools have resulted in rising student achievement. Setting goals can create an incentive for students to work harder both in and out of the classroom. And furthermore, these students take greater pride in their accomplishments.
The key to success is breaking down goals into achievable steps and measuring progress. When students set goals that are too high, they may feel defeated if they do not accomplish them. Many schools use “SMART” goal-setting forms, an acronym which stands for “setting Specific, Measurable, Attainable goals with clear Results in a set Time frame.” Schools have observed rising test scores as a result of this focus on goals. But not only test scores have been affected. Goal-setting is a skill that motivates students to work hard in areas that they care about. While one student may want to get an A in math, another might strive to make the basketball team. Either way, accomplishing goals helps students believe in themselves and maintain a positive attitude that can be a high predictor of college success, according to senior scientist Shane Lopez of Gallup, Inc.
Goals are an easy way to get students excited about achievement. Even struggling students can become confident learners if they track their success by taking small steps toward improvement. How do you use goals to motivate students in your classroom?
Now that we’re approaching April, most of my colleagues are in over-drive trying to prepare their students for the state tests that are given in early May. One of my goals as a teacher-leader is to help my colleagues recognize that April is not meant to be “test-prep month”. Unfortunately, with more and more pressure being put on teachers to ensure that their students pass the test, educators feel the need to do anything and everything to get their students ready. While I understand the stress teachers feel, I would prefer if April were not a month solely dedicated to test preparation. Instead, teachers should strive to continue with normal daily instruction and include test-prep activities that consume only minutes of the daily routine.
To be successful, teachers need a lot of up-front planning to ensure that students are well-prepared for the tests far in advance of April. This is not an easy task, but the idea is that if students are taught the curriculum throughout the year, they should be prepared for the end-of-year test. The challenge is that most of these tests are not at the end of the year. Instead, they are about 6 weeks before the last day of school, so teachers are required to teach ten months worth of content in eight-and-a-half months.
This is a problem I have yet to solve. Some research suggests starting the year’s curriculum immediately following the prior year’s state tests. So essentially, students would start learning 5th-grade content at the end of their 4th-grade year. This has its merits, but it presents problems when students change schools or districts. It seems that the only viable option is to really plan out the year so that 10 months worth of content can be covered in minimal time. This may require strategic lesson planning and closely following the curriculum, not the textbook. Most textbooks cover far more than teachers are required, so it is important that teachers thoroughly evaluate their curriculum to be sure they aren’t teaching a lot of extraneous content. Lesson-planning in this way is likely to take several years to master, but it is necessary to ensure students are well-prepared for the test. And, it will allow teachers to spend the month preceding the test teaching as they have all year and simply integrating test-prep tips and last minute quick-reviews to best prepare all students.
Just this morning, I began filling out my bracket for the annual NCAA Basketball Championship pool. While not everyone is a fan of basketball (myself included), it seems that almost everyone participates in a March Madness pool. I think it’s because there are so many possibilities that even the most skilled sports analyst can’t possibly pick every winner. So, anyone can do a little educated guessing and end up victorious. As I began making my selections, I thought about all of the possible combinations of tournament winners. Then, I glanced at the given odds and began analyzing those numbers. Before long, I realized that I was doing all sorts of math that I hadn’t before recognized.
As it turns out, there is a lot of math evident in the NCAA tournament. We all know that getting kids excited about math and helping them connect to the concepts is one of the biggest battles that math teachers face. And here I am sitting at my kitchen counter looking at some of the most interesting math problems I’ve seen – and as I mentioned, I don’t even like basketball. Imagine the excitement of a middle-school student when they realize that this yearly event can help them learn math!
So, where is the math? Well, it depends on the level of your students, but how about just asking them to figure out the number of different completed brackets that are possible? Or, what about finding the probability that a team will end up in the “Sweet Sixteen”, “Elite Eight”, and so on. Then, think about the odds...which team has the greatest odds? The worst odds? As the tournament commences, you could have students track points of a particular team or a particular region, or even individual statistics of teams or players. Do a little internet research, and you’ll find all sorts of activities related to math and the NCAA basketball tournament. I even found a web quest which covers lots of the categories of math lessons that I mentioned.
Remember, you don’t always have to follow the book or create fictitious mathematical scenarios for your students. Think about what’s going on in their everyday lives and I’ll bet you can come up with some interesting contexts for math problems. This is just one topic that is sure to have many of your kids excited to do the math!
Earlier this week, Pi Day was celebrated around the nation to pay tribute to the mathematical constant that many of us learned in geometry. Of all the activities I read online, these are some of my favorites:
- In Massachusetts, hundreds of apple pies were delivered to math and science teachers within a 3.14-mile radius of the Raytheon headquarters in the city of Waltham.
- At Princeton University, where the day is also celebrated as Albert Einstein's birthday, they had a week-long Princeton's Geek Freak celebration. On hand were plenty of pies and many who dressed up as Einstein.
- A musician, Michael Blake, put mathematics to music by interpreting pi to 31 decimal places and shared his creation online. Listen for yourself, pi sounds pretty good!
Watch the video
- In Seattle, students created links out of construction paper, all with a digit of pi. To celebrate pi, they took a group photo in the gym – showing off 5,000 linked digits!
Take a look at their impressive creation
What are your favorite Pi Day celebrations? Did you do something special this year?
Recently, I was speaking with a soon-to-be college graduate about her preparation to enter into a classroom in the fall. While her confidence was evident, she claimed that she wasn’t convinced that she was trained in the appropriate areas to begin teaching middle-school math. Upon delving deeper, I recognized that she has many of the same feelings that I once had. As a math education major, I took many high-level math courses that included content far beyond the scope of high school math courses. In fact, the bulk of my training encompassed these higher level math courses, while few courses dealt with math education pedagogy. In the years since I have graduated college, it seems that little has changed in terms of what courses are required.
Specifically, my conversation with this young teacher revolved around methods for differentiating instruction and dealing with students who speak English as a second language. These are two prominent elements of today’s classroom, yet little training is offered to prepare students for such challenges. A recently published article, RTI Makes Few Inroads Into the Nation’s Education Schools, focuses on the lack of training that teachers receive on RTI (Response to Intervention), yet another hot-topic in education. Teachers are expected to understand the RTI model, yet they aren’t provided RTI training.
With so much pressure on teachers to increase students’ test scores and to take responsibility for the progress of their students, it seems unfair that teachers may enter the work force ill-prepared. While some education programs may be addressing this issue, many are not. This is a situation that needs to be addressed if all teachers are expected to be accountable for student progress. As a veteran teacher, perhaps I can help new teachers improve teaching practices in the aforementioned areas. It won’t alleviate the problem, but it’s a small step in the right direction to ensure new teachers enter the classroom prepared for the challenges that they will face.
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I’m a literature nerd.
My bookshelves sag under the weight of novels and more novels. I’ve modernized Hamlet’s soliloquy for fun. If I could, I’d snuggle with lines written in iambic pentameter.
With so much nerdiness, you’d think I would have figured out that iambic pentameter screams math.
For those not in the know, iambic pentameter is a poetic measure where there are (generally) 10 syllables in a line of poetry. Each line has a rhythm of “da-DUM.” If you’ve read a Shakespearian sonnet, you’ve seen iambic pentameter.
In an article written by Joe Pagano, he explains how you can take a sonnet and convert it into math by applying “0-1” to every “da-DUM.”
“For those of you who recognize this pattern, you notice that we have converted the meter of the sonnet into a binary pattern of digits. By converting the sonnet into this binary pattern, we can spot instantly whether each line of a sonnet fits rigorously into the iambic structure or not. For any line that does not alternate between 0's and 1's, with five of each in each line, would technically fall outside this structure.”
So, if we take the line “Shall I compare you to a summer’s day?” from Shakespeare’s Sonnet 18 and convert it to binary, it will look like 0-1 0-1 0-1 0-1 0-1.
Not all lines in iambic pentameter follow its rigidity. Take the opening line to Hamlet’s soliloquy: “To be or not to be, that is the question.”
How does that look in binary?
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Many thanks to our friends at MetaMetrics Inc. for contributing a useful guest blog entry about how teachers can match all students to the right instruction with the Quantile Framework for Mathematics.
The Quantile® Framework for Mathematics
is a tool teachers can use to make student test results useful at the classroom instruction level. A student’s Quantile measure (test score) provides information about which mathematical skills students are ready to learn in the classroom. These skills are called QTaxons. Once a teacher knows a student’s Quantile measure, the teacher knows which QTaxons the student is ready to be introduced to in the classroom. Underlying each QTaxon is a knowledge cluster that offers classroom teachers a wealth of information about the skills that come before the QTaxon skill and those that follow it. This information can be tremendously helpful in guiding decisions about instructional strategies.
A QTaxon is linked to prerequisite, supplemental and impending QTaxons that illustrate the developmental and inter-connective aspects that are so important in the study of mathematics. A prerequisite QTaxon includes the skills and concepts that should be addressed or mastered by the student before instruction on the focus QTaxon. A supplemental QTaxon includes skills that can enrich a topic or help teachers and students make connections across the spectrum of mathematical concepts. An impending QTaxon can provide insights into the levels of mathematics skills beyond the focus QTaxon.
Below is an example of a knowledge cluster in the Quantile Framework using a focus QTaxon about 'unit rates'.
QTaxon: “Calculate unit rates to make comparisons.”
This QTaxon has a Quantile measure of 830Q. (Each QTaxon has a Quantile measure that estimates its difficulty at the introductory level.)
- Use proportional reasoning to solve problems. (530Q)
- Identify equivalent decimals and fractions at the symbolic level, including simplifying fractions. Explain the equivalence. (710Q)
- Write a ratio to compare two quantities. (210Q)
- Convert measures of length, area, capacity, weight, and time expressed in a given unit to other units in the same measurement system. (820Q)
- Describe the probability of an event using a fraction or ratio. (440Q)
- Determine the ratio or rate of change of a relation given a table or graph. (810Q)
- Use dimensional analysis to rename quantities or rates. (950Q)
- Use scale factors to reduce and enlarge drawings on grids. (990Q)
With some Quantile information – the student’s Quantile measure, the Quantile measure of the focus QTaxon, and the Quantile measures of the prerequisite, supplemental and impending QTaxons – the classroom teacher can use assessment results to target instruction that addresses the needs of various populations of students in the classroom.
Consider the possibilities! By identifying the level of mathematics ability for students, educators can differentiate instruction, forecast performance on new material or assessments and benchmark progress throughout the year. The supplemental QTaxons in the knowledge cluster provide instructional tips on making connections across content strands and enriching instruction. The knowledge clusters found on the Quantile website at www.quantiles.com
are one aspect of the free materials available to teachers, students and families.
Welcome to Alicia Gregoire, our newest writer for the Math Hub blog.
As a member of the Sesame Street generation, I love it when entertainment and education come together. My favorite teachers were the ones who were able to incorporate pop culture into the every day. With this in mind, it’s no wonder I still harbor a schoolgirl crush on the TV show, Square One.
Created by the same people responsible for Sesame Street, Square One focused on a variety of math concepts in short sketches. One of my favorite segments dealt with the math magician, Harry Blackstone, Jr.
Harry Blackstone, Jr. would perform a magic trick for a group and then explain how it was done. Below you can see one of his tricks involving a twenty-dollar bill.
What are some ways you entertain while you educate?
A cluster of new studies out of UMass Amherst suggest that the presence of female instructors and role models in math and science can serve as a “social vaccine” that protects female students’ interest in those fields. You can read a nice description here.
One part of the cluster of studies looked at women in a university math course. Their attitudes and performance both improved significantly over the course of a semester when the professor was female: the percentage of female students asking questions in class or seeking help at office hours increased appreciably when the professor was female and decreased when the professor was male. In another part, even the barest presence of a female role model – a female greeter wearing a shirt reading "E=mc2" – improved the women’s performance on a difficult math test.
This study addresses one enduring puzzle about girls and STEM: why are women so outnumbered in STEM careers, when at the high school level they are equaling or outperforming their male peers? There’s still so much female attrition along the way – why? Well, role models dwindle as the girls advance, and as these studies suggest, this is a strong signal to young women that they do not belong there.
I like the idea of a social vaccine, because I think this is a two-part problem, at least. Yes, girls are probably getting subtle negative messages about STEM from the world around them. But one thing this study indicates is that girls, more than boys, are highly susceptible to both positive and negative messages, and we need to take extra care to fortify them against the negative ones.
I for one think that we women are wired to be super tuned-in to our environment, and that it’s a great trait. But maybe in the case of advancement in STEM, it’s hurting us.
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Insights on how neuroscience can benefit educational practice and policy were recently published in the "Brain Waves" report by the Royal Society.
Three key messages came out of the report:
- The need for a common language between scientists and people in the practice of education.
- A recommendation for teacher training and continued professional training on neuroscience, and how it is relevant to learning.
- The relevance of neuroscience in the development of new adaptive technology that can be used in the classroom to enhance learning and teaching.
The report provides a (highly readable!) crash course on aspects of neuroscience that can be applied to education. For example, knowing about the brain's neural responses to challenges and rewards could influence the design of a curriculum that provides frequent feedback and formative assessment. In discussing how adaptive technology can help, the article states: "Even where successful teaching approaches have been developed for learners who cannot keep up with the mainstream classes, widespread implementation may fail because there are too few specially trained teachers, and the level of frequent and individual attention that many learners need is unaffordable. Teachers would provide expert feedback on progress based on, but going beyond, the feedback from the adaptive software."
Do you think it's important for educators to know the research behind brain-based educational products and software? Should neuroscience be part of teacher training and professional development?
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