Vermont Council of Teachers of Math eNewsletter! This newsletter is now being seen by about 700 math educators all around VT, and many have registered since the first issue last month. If you know someone who might benefit from this newsletter or blog, please feel free to forward this along to them and have them visit our blog site 'Math in Vermont'. Our mission is to have Vermont be one interconnected math network, sharing our ideas and strategies, and showing how we should all be cognizant of each others work in all grade levels. To date, about 40% of those on the mailing list work with students under age 11 and this gives us all an opportunity to appreciate what they are doing in the classroom. So if you would like to submit an article (as a few members have done in this newsletter) or have comments or suggestions, please send it along to me . - David Rome, VCTM eNewsletter Editor
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In this issue:
- President's Message- Jason Cushner
- The Myth of Lagging U.S. Schools by Alfie Kohn
- A Device to Identify and Calm Math Anxiety
- Presidential Award Winners and Finalists Announced
- The Price is Right- Free Mathematicians in Your Classroom
- The Greater Burlington Math League
- Book Review: The Impact of Identity in K-8 Mathematics; Rethinking Equity -Based Practices
- Profile: Q&A with VCTM President Jason Cushner
- Article: Helping Students Work Through Mathematical Conjectures
- Special Winter Offer for Girls by the Governors Institute
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President's Message January 2014
Happy New Year to you all! As I work with different folks around implementing the Common Core State Standards, I am struck by the gravitational pull towards the content standards instead of the Mathematical Practices. So much of our curriculum and resources have been focused on content, while part of the shift of Common Core in theory is to reduce the amount of content in a year to have the space to focus on the Math Practices .
Content may be more aligned with what most of us have been doing and is easier to measure. That being said, it’s not necessarily what is best in preparing our students for their futures. The question is how to go about emphasizing the Mathematical Practices. If you have great methods, please share.
One method I learned about through reading Ben Blumsmith’s Blog is getting students to summarize each others ideas and critique them, as opposed to the teacher jumping in as the expert and saying whether something is right or not. Having students summarize each others theories both increases skills in mathematical communication and can serve as an easy lead in to mathematical discourse.
Have a great new year and stay in touch about how we can support you in math excellence for all.
Jason Cushner
VCTM President
Program Coordinator Big Picture South Burlington
Rowland Fellow
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We're Number Umpteenth! The Myth of Lagging U.S. Schools Copyright 2013 by Alfie Kohn. Reprinted with the author's permission. For more, please visit www.alfiekohn.org.
Attacking the quality of education in America has become a sport that has been spreading for decades. Educational topic writer Alfie Kohn recently put several of the critics arguments in context, and should give us all a moment to step back and contemplate the larger picture of what is really going on. To read the full article, go to the posting following this one below and please feel free to comment at the bottom of the article and even get a response back from the author himself. A brief excerpt from the article:
"A dedicated group of education experts has been challenging this canard for years, but their writings rarely appear in popular publications, and each of their efforts at debunking typically focuses on just one of the many problems with the claim. Here, then, is the big picture: a concise overview of the multiple responses you might offer the next time someone declares that American kids come up short. (First, though, I’d suggest politely inquiring as to the evidence for his or her statement. The wholly unsatisfactory reply you’re likely to receive may constitute a rebuttal in its own right.)
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A Tool for Taming Fear and Anxiety in Learning Math, Submitted by Sue Abrams, Montpelier High School
We all know that in the ideal world of math instruction, good lessons are those in which students construct their understanding of math concepts based on experiences with models, engaging real world problems, etc. Good, probing questions by the teacher or classmates can also help a student attain those "aha" moments that are essential for true learning.
However, students arrive at our doors with emotional barriers that can shut down their openness to engaging in the learning process in any meaningful way. Some students have had years of accumulated negative feelings associated with learning math, and others appear successful but are extremely anxious about their math ability nonetheless.
With this in mind, I was prompted to tickle the edge of this math anxiety by trying a new tool that is often used by people in the medical field to help people with anxiety and stress. It's called the Inner Balance Trainer sold by the Institute of HeartMath in Boulder Creek, California. This module attaches to an iPad or iPhone to activate an app which allows a student to monitor in real time their HRV, heart rate variability, as they practice breathing techniques with the aid of a breath pacer. The strength of this is the very visible feedback students get when they see their HRV change from very random jumping around to looking much like a smooth sine wave in a matter of minutes. Furthermore, it takes only about five minutes or so per day to make a significant impact.
With the help of a sizable grant from the Institute of HeartMath and another grant from the Montpelier High School Boosters Club, I was able to purchase a set of 22 Inner Balance Trainers and have begun to introduce them to students in math classes. Our students will have the option to participate in a research project over a few months, while others will drop in during our 15 minute recess to try them out or just use them before assessments or even regular math lessons. Sue Beem, another member of the math department, is a collaborator on the project, and although the results are not yet known, we are excited to get right to the heart of the anxiousness or stress students can feel in math class by potentially helping them feel the inner balance needed to open the door to learning. You are welcome to get in touch with me if you have questions at suea@mpsvt.org.
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Two Vermont Math Teachers Chosen for Presidential Teaching Award for 2012 as 2013 Finalists are Announced
Joy Dobson and Mary Ellis were selected for the 2012 Presidential Award for Excellence in Math and Science Teaching (PAEMST) for teachers in grades K-6 for 2012. Joy Dobson has served as an educator at Weybridge Elementary in the Addison Central Supervisory Union for 20 years. She has taught single and multigraded classrooms of kindergarten through second grade. Mary Ellis has been an educator at Enosburg Elementary School for the past 15 years. Currently a fourth grade teacher, Mary teaches science, social studies, and mathematics to her homeroom class and provides mathematics instruction to another fourth grade class each day. She has taught fifth and sixth grade and served as the school’s Mathematics Coach. In her role as coach, she modeled lessons, collected and organized classroom data for analysis, and collaborated with teachers to improve instruction.Joy provides an exceptionally strong mathematics program and ensures that students have the mathematical language, concepts, skills, and models to approach and apply mathematics with confidence and clear thinking. She is dedicated to not only addressing the needs of all students, but also to ensuring that their learning meets the very highest expectations. This work is founded on her unfailing belief in each child as a capable thinker and learner. As a teacher leader, Joy is held in high regard throughout the supervisory union. She serves as a district-level Math Leader, collaboratively designing and implementing professional development for teachers, developing curriculum, and serving as a studio teacher. As a mathematics mentor, Joy is known for her open-door policy, encouraging teachers to observe, ask questions, and grow professionally while experiencing a multigraded classroom and differentiated instruction with high academic expectations. She has a B.S. in elementary education from Nyack College and an M.Ed. in education from the University of Vermont. She is certified in elementary educationA lifelong learner, has participated in many mathematics and technology professional development opportunities. She has a deep understanding of elementary mathematics content and research-based instructional strategies. She is very involved in the Franklin Northeast Supervisory Union. She has served on task forces to develop mathematics curriculum and assessments, has facilitated districtwide in-service meetings, and is part of a district committee focused on the implementation of the Common Core State Standards for Mathematics. Mary has a B.A. in psychology from Boston College and an M.Ed. in curriculum and instruction from the University of Vermont through the Vermont Mathematics Initiative. She is certified in elementary education.
Each year, a national committee of distinguished scientists, mathematicians and educators recommends up to 108 teachers to receive PAEMST awards - up to two teachers –mathematics or science- from each state, the District of Columbia, Puerto Rico, the U.S. territories as a group, and the schools operated in the United States and overseas by the Department of Defense Education Activity. The awards program is administered by the National Science Foundation (NSF) on behalf of the White House. PAEMST awardees receive a $10,000 award, a Presidential certificate and a trip to Washington, DC, for a series of recognition events, professional development activities and an awards ceremony. Congratulations to Joy and Mary!
Meanwhile, the VCTM has announced the Vermont state finalists for the 2013 PAEMST awards for grades 7-12. They are Sue Abrams (Montpelier High School), Erin Danner (Mill River Union High School), Julie St. Martin (Champlain Valley Union High School), and David Rome (Burlington High School). All four finalists were recognized at the Association for Teachers of Mathematics of New England fall conference in November. They are now eligible to receive a PAEMST award, the nation’s highest honor for U.S. mathematics and science teachers for grades K-12.
The 2014 PAEMST will honor mathematics and science (including computer science) teachers working in grades K-6 and nominations are open right now, but will close on April 1, 2014, Visit the PAEMST website for more details.
The 2014 PAEMST will honor mathematics and science (including computer science) teachers working in grades K-6 and nominations are open right now, but will close on April 1, 2014, Visit the PAEMST website for more details.
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The Price is Right- Free Mathematicians in Your Classroom from John Devino of the Vermont Math Coalition
As classroom teachers, we are continually looking for ways to make mathematics relevant and meaningful to our students. This would be a good time to bring a mathematician to your classroom, who is capable of reaching your students. With the weather being a “hot topic” (sorry!) lately, Janel Hanrahan’s presentation entitled “Mathematics and the Atmosphere” seems like a natural.
The Vermont State Mathematics Coalition has 26 programs available for you and your students. It all begins with an e-mail or phone call to one of the presenters.
Go to http://vtmathcoalition.org
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The Greater Burlington Math League by Janet Soltau, Colchester High School
The Greater Burlington Math League has been competing in the greater Chittenden County area for over 50 years. The league, founded by Tony Trono of Burlington High School in 1961 has had a varying number of teams of the years, but currently has 12 schools participating with approximately 240 participants. Every month teams gather at a different school to compete in 5 different categories: Arithmetic, Geometry, Algebra, Advanced Math, and Team. Topics within the categories vary from meet to meet, with the team test including topics from each of the categories, which 5 students get to work on together. The majority of the season students do all math with out a calculator (with the exception of the team test), which is a great mental challenge.
In recent history, Essex and South Burlington, have traded the title back and forth. Awards are given to the top students in each category at the end of the season, and the top ten individuals overall. The top team this year will win $150 sponsored by the Mu Alpha Theta, a mathematical honor society.
Current participating high schools are BFA St. Albans, Burlington, Colchester, CVU, Essex, Milton, Missisquoi, Mt. Abe, Mt. Mansfield, Rice, South Burlington, and Vergennes. Past participants have included BFA Fairfax, Middlebury and Winooski. For more information, contact Janet
Math league coaches also encourage students to participate in the Vermont Mathematics Coalition Talent Search (http://vtmathcoalition.org/
In recent history, Essex and South Burlington, have traded the title back and forth. Awards are given to the top students in each category at the end of the season, and the top ten individuals overall. The top team this year will win $150 sponsored by the Mu Alpha Theta, a mathematical honor society.
Current participating high schools are BFA St. Albans, Burlington, Colchester, CVU, Essex, Milton, Missisquoi, Mt. Abe, Mt. Mansfield, Rice, South Burlington, and Vergennes. Past participants have included BFA Fairfax, Middlebury and Winooski. For more information, contact Janet
Math league coaches also encourage students to participate in the Vermont Mathematics Coalition Talent Search (http://vtmathcoalition.org/
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The Impact of Identity in K-8 Mathematics; Rethinking Equity Copyright © 2013 by the National Council of Teachers of Mathematics, Inc.,www.nctm.org
In this book by authors Julia Aguirre, Karne Mayfield-ingram, and Danny Bernard Martin, the math community of parents and teachers, rather than just the latter, in the success of the students. Among the highlights of the book:
- Mathematics Identity is the dispositions and deeply held beliefs that students develop about their ability to participate and perform effectively in mathematical contexts and to use mathematics in powerful ways across the contexts of their lives.
- Mathematics is both the gateway and the gatekeeper to learning opportunities in school and beyond
- It is critical to focus on finding ways to build on the resilience created by a child’s life conditions rather than on the conditions themselves; focus on learning not labeling.
- Feedback that students receive on assessments can contribute positively or negatively to a child’s disposition about his/her ability to learn mathematics based on how the feedback is delivered, what information is shared with the student, and whether or not the students is involved in self-reflection.
- How a child’s progress is communicated to parents can affect how they see their child as a learner of mathematics.
- Regardless of family income, education, or cultural background if parents are involved in their child’s education those students experience higher academic achievements than those whose parents are not involved
- Additional Authors to consider on this topic: Jo Boaler, Vi Hart, and Robert Q. Berry, III
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Profile: Q&A with VCTM President Jason Cushner
In an effort to better know the people involved with math in Vermont, we being offering interviews with VCTM Board members in each issue of our eNewsletter.
David Rome (DR): Tell us a little bit about yourself- where are you from and where have you taught?
Jason Cushner (JC) :I love to find innovative ways to teach math. I’ve taught math through building a low income health clinic, calculating water flow for the Colorado River, building a boat, and studying discrimination. I’ve taught in multiple schools in Colorado and Vermont (and even taught English in Turkey for a while). I also enjoy rock climbing, backpacking, and going on adventures with my kids (2 & 5). I have been on an international climbing expedition to climb an unclimbed peak in Pakistan. I met my wife teaching an integrated Calculus and Physics course
DR: You are also involved with the PAEMST (see above article) - have you been a recipient?
JC: Yes I won the Presidential Award in 2003 in Colorado and was one of 4 teachers asked to testify for congress on STEM education. I had no idea how nice you had to dress for all the events until a few days before when they sent me the descriptions and realized that I didn’t own nice enough clothes for the events. So I went to the thrift store and bought some nice clothes. Right before leaving for the opening events and possibly meeting the president my wife called me back and realized I had the $4.99 price tag still stapled to my suit.
I also am National Board Certified, Outstanding Mathematics Teacher for the State of Colorado, and a current Rowland Fellow.
DR: Tell us why you are involved with the VCTM and what you see as its role for Vermont math teachers.
JC: I’m involved with VCTM because it’s great professional development for me and I think it’s key to have a support network for engaging and inspiring students in math. The role of VCTM for Vermont math teachers is to:
· Connect math teachers to provide professional support· Be a hub of resources for math education· Support teachers and administrators in improving math education in the state
DR: What is the program that you implement at South Burlington HS, and what type of student does it reach?
JC: I’m currently program coordinator for the Big Picture program at South Burlington. It’s where student create individuated curriculum around their interests and internships. So we have students interning at a Biomedical lab at UVM, elementary school math classes, graphic design studios, farms, computer networking firms, and much more. Students have an adviser who then helps them create individualized learning plans to deepen learning.
The program attracts the full spectrum of students. Last year we got students who got a 4.0 GPA in AP classes and we had a student who came in with a 0.4 GPA (not easy to do & that student is a nationally published blogger and has presented at multiple education conferences).
DR: What do you see as the biggest challenge for teachers in general, with the rolling out of the Common Core?
JC: Part of the philosophy of the Common Core is a reduction in content so that there is space to work on the Mathematical practices (problem solving, persistence…) and those skills are not as easily measured in content. I think schools and the media need to give teachers the time to work on how to better integrate the Mathematical Practices into curriculum and share success that are happening in these areas across the state.
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Article: Helping Students Work Through Mathematical Conjectures
In this thoughtful article in Teaching Children Mathematics, Amy Hillen and Tad Watanabe (Kennesaw State University) say that an important Common Core math reasoning skill is making conjectures and assessing them based on evidence. They suggest the following 60-minute lesson for elementary students:
- The teacher displays 1-9 on the board: 1 2 3 4 5 6 7 8 9- The teacher picks the number 4 and writes it on another part of the board.- The teacher calls on a student to pick another number – 8 is chosen.- The teacher writes the 8 by the 4.- “With these two numbers, which two-digit numbers can we make?” the teacher asks.- 48 and 84- “Which is larger?” 84. The teacher writes the numbers using vertical notation: 84 - 48- The teacher asks students to subtract, and the answer is 36.- “Let’s try this with some other numbers.” This time, a student picks the first number, 7. The teacher picks the second number, 3 (making sure the difference is going to be 36).- The teacher again sets up the subtraction problem: 73 – 37, and the answer is 36.- “It’s the same!” students exclaim. “It’s always going to be 36!”- The teacher explains that this is a conjecture and writes it on the board – “If two different numerals are picked randomly to form 2 two-digit numbers, the difference will always be 36.”- “I wonder if this will always be true,” says the teacher. “How can we find this out?” Students suggest some ideas, and the teacher has students spend ten minutes working with a partner – just enough time for them to come up with only one or two possible combinations (students were given a template to set up the subtraction problems).- Students post their subtraction problems on the board.- Everyone looks at the examples (duplicates are removed), and students notice that some problems have answers other than 36. Their initial conjecture was not true.- Now students are asked to work in pairs to revise their initial conjecture and formulate new conjectures based on the set of subtraction problems posted on the board.- Some students are boggled by the number of problems on the board and are prompted to sort them into groups with the same answer and asked, “What do you notice about the problems whose difference is 36?”- Now the whole class discusses different conjectures. One student says that when the numbers chosen are next to each other, the answer is always 9. The teacher has the student clarify what “next to each other” means.- Another student says that when the chosen numbers are separated by one number, the answer is always 18.- Now students work in pairs again to try to refine the conjecture. Students often notice that the difference will always be a “nine fact” – a multiple of nine; that all the problems that have the same difference involve numerals whose difference is the same; and the difference will always be a product of 9 and the difference between the two.- Students are challenged to explain to a skeptic why these conjectures will always be true. The teacher asks, “How do we know that there is not a problem that we don’t have on the board whose difference is not a multiple of 9?” One approach is “proof by exhaustion” – trying all the possible problems. But is there another way? This might lead to organizing examples in a systematic way.- The teacher concludes the lesson by pointing out the important reasoning-and-proving work they have done, the importance of perseverance when the initial conjecture proved false, and how that led to a more sophisticated finding. In fact, conjecturing and proving (and disproving) are the essence of doing mathematics.
To see a delightful video of a Japanese teacher teaching this lesson, go to (free registration)
“Mysterious Subtraction” by Amy Hillen and Tad Watanabe in Teaching Children Mathematics, December 2013/January 2014 (Vol. 20, #5 p. 294-301),http://bit.ly/1hz3128
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If you are not on the MathNet mailing list, then you might not have heard about this offering from the Governor's Institute that was circulated recently:
Hello and Happy New Year! I’m writing from the Governor’s Institutes of Vermont. Because we always have so many Math Institute applicants we can’t serve in the summer, we are holding a winter event just for high school advanced math fans. This residential weekend exploration of math is just for girls and will be held at Goddard College February 7-9, 2014 (Marlboro, VT) with lead faculty member Marlboro professor Julie Rana. Student applications are being accepted now on a first come-first serve basis.Young math lovers (male and female) may also be interested in our brand new Astronomy strand at the second Winter Weekend, where participants will learn how to apply math, computer science, and graphic design to map the stars. We will also offer Engineering and Information Technology topicals. More information about GIV is available at www.giv.org, and information about Winter Weekend specifically can be found at www.giv.org/winter.The registration process for GIV Winter Weekends is much briefer than our summer programs, since they are weekend-long programs, and as always, scholarships are provided to any students with financial need. Interested students may apply directly to GIV (rather than through their schools as they do in the summer). Please encourage your students to register quickly since we do expect the program to fill up! Applications can be mailed to the address below or emailed to Valerie@giv.org.Karen Taylor Mitchell, MPA, Executive Director Governor's Institutes of Vermont, 4049 Williston Road, #4, South Burlington, VT 05403, 802-865-4GIV, www.giv.org
