Last Tuesday, President Obama hosted a science fair at the White House to underline the importance of S
ngineering, and M
athematics learning, or STEM education
. At the fair, the president proposed an $80 million increase in federal funding directed toward math and science education
. A large chunk of that money would be used to train specialized math and science teachers. Some would function to incentivize math education at the elementary, middle, and high school levels. While this proposal, along with the rest of the president’s 2013 budget plan, requires approval by Congress, it acknowledges STEM’s critical importance and potential for growth. In addition, President Obama stressed the positive impact of many educational grants from private sector businesses and organizations.
By taking part in science fairs and other STEM activities aimed at exploring practical problems, students become engaged with the subjects and are more likely to pursue them at a higher level. And since many students find math to be a particularly difficult subject to grasp, focusing funding on teacher training could boost student success markedly. As the Common Core makes its debut in classrooms, U.S. math education is already in a state of evolution. Greater emphasis on STEM and better teaching practices will hopefully increase math’s popularity with students.
The President’s overarching goal of promoting and strengthening STEM education is to encourage students to pursue these subjects at the collegiate level and in their careers. Currently, only 40 percent of math and science majors complete their degree, and projections show that the country will need one million college graduates in the next decade to fill anticipated job openings requiring math and science skills. We need to attract students into these fields, and the government’s commitment to STEM is encouraging. With our country’s rapid technological growth, it’s important to keep math education up-to-date both in its content and how it is taught.
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.
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.
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
Each day Madame X,
keeper of the emporium,
raises or lowers each price --
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,
is seeing the truth
in The Book
is as elegant,
as could be.
as should be.
as it is.
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.
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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Jotting down worries before an exam can help students perform better academically. New research, published in the journal Science this month, suggests that this short exercise can especially be helpful to those who routinely crack under pressure.
According to the journal's online news, here's what happened in the experiment:
"In the study, the researchers asked college students to take a math exam covering material they had never seen before. Then things got even more stressful. The students were given a second exam, but this time they were told that they would receive money if they passed. They were also told that they had a partner who had already done well and who would be let down if they failed, and that they would be videotaped while taking the test so that their teachers and friends could watch."
The results? Students who wrote about their worries scored, on average, 5 percent higher on the second test than on the first. And here's the shocker: the other students did worse on the second test than the first by 12 percent! In explaining why this happened, one of the researchers, Sian Beilock, explained: "Writing about their worries allows the students to reexamine the testing situation and reappraise it. This frees memory resources and increases the ability to focus."
The study provides one more piece of the puzzle in the development of interventions for students with test anxiety so that the exam is more indicative of their ability.
http://www.flickr.com/photos/21560098@N06/ / CC BY 2.0
The release of the 2009 PISA (Programme for International Student Assessment) results last month prompted another round of hand-wringing over the United States' mediocre performance. Shanghai (China), South Korea, Finland, and Singapore topped the charts in math. The United States ranked 17th, slightly above the average of other advanced OECD (Organization for Economic Cooperation and Development) members. The latest PISA results followed the publication of the report U.S. Math Performance in Global Perspective, which summarized the importance of creating a population of high mathematical performers to feed a growing STEM-based economy. Sadly, the report concluded that the U.S. is lacking compared to its international peers. There’s an accessible article articulating the findings of the report at Education Next.
However, not everyone thinks the situation is so dire. The National Education Policy Center (NEPC) at the University of Colorado has challenged the methodology of the Harvard and Education Next report. The NEPC review calls the report’s comparison across countries and tests (PISA versus NAEP) “deceptive”, offering “essentially no assistance to U.S. educators seeking to improve students’ performance in mathematics.” Those sound like fighting words to me. Noted economist Robert Samuelson joined the fray with a recent article in The Washington Post, where he suggested that schools in the United States aren’t as bad as they are often depicted. Of course, that piece prompted a response in Education Next.
What’s the story? Are American schools short-changing us in the competition for top mathematical talent or not? Well, we can certainly do better, and we should seek to learn from countries like Singapore that have turned a largely illiterate population at the time of its independence in the 1960s into one of the world’s top academic and economic performers. And one area where everyone agrees (I think) is the need to remedy the performance gap among sub-groups in the United States. Blacks and Hispanics continue to lag behind whites. While some may argue that a focus on raising the bottom has taken resources from elevating the top, I certainly wouldn’t want the reverse.
http://www.flickr.com/photos/maaorg/ / CC BY 2.0
This week, I came across an article that provides insight into some of the struggles that math teachers face. CNN's article, Subject Matters: Students Struggle with Math Fundamentals discusses some of the challenges that math teachers encounter in today's educational environment.
The author, Sally Holland, mentions three areas of struggle and offers supports through examples provided by teachers around the country:
- Students rarely have a deep understanding of the math basics that are necessary for further math study. Because students are required to learn so many topics in a given school year, they tend not to master any skills. Instead, they gain surface-level understanding that enables them to pass the test, but doesn't necessarily enable them to learn higher-level math in subsequent years.
- Teachers have to deal with a variety of student learning styles. Many teachers have developed one method of teaching that may not meet the needs of the majority of students in the class. Now, with the heightened awareness of different learning styles, teachers must be cognizant of how best to meet the needs of all learners.
- The article stresses the need for teachers to incorporate math into the real world. Unfortunately, with so much pressure to learn a great number of skills for state tests, teachers don't always have time to incorporate real-world activities until late in the school year. Even so, it is important to help students recognize how math is needed for so many activities outside the classroom.
Each of the challenges mentioned in the article is likely to arise in your school or district. The important thing for us to consider now is how to overcome these challenges.
Please share the techniques or strategies you use to overcome these challenges. How are you ensuring that your students leave school with the knowledge, skills, and disposition that they need to succeed in our mathematical world?
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Like many of you, I am in the process of preparing next year’s budget and determining what materials will be needed to support student instruction. In addition to our typical order, we are thinking about investing in new elementary math textbooks. In NJ, the Common Core Standards were adopted and implementation of the new standards for Kindergarten through Grade 2 will begin in September. We feel it is appropriate to introduce a new textbook that will more closely align with the new expectations.
One of the challenges of textbook adoption is recognizing what comprises a quality textbook. Teachers tend to look for features with which they are most comfortable. These preferred features are likely part of their current textbook series, so teachers often select a textbook that is almost identical to the one they are currently using. In some cases, this is a completely acceptable outcome. However, we do want teachers to look for features that will be most beneficial for their students, not just those that keep them in their comfort zone.
To facilitate this process, I am going to use a textbook evaluation checklist with all of my teacher colleagues. This checklist provides un-biased suggestions of elements in the textbook that will be beneficial for all users. You may choose to use a checklist that you find online, or you may create a checklist that is specific to your district. Either way, it’s helpful to provide teachers with a guide that provides characteristics to look for in a new textbook and allows teachers to rate elements based on their importance. I found this checklist online, and I plan to use it as a template for creating a checklist that will meet our district’s needs. I think this tool is one that will increase teacher awareness as they look at textbooks, and I’m sure that teachers will emerge from the process confident that they selected a textbook that includes all the features that are necessary to increase student achievement.
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