President’s Message- Are We Keeping Up?

By Rob Lukasiak

I can’t say that I travel very much, although over the past few weeks I have made trips to Nashville and Pittsburgh – both work-related.  The Nashville trip was to attend and co-present at the 2018 iNACOL Symposium.  This was my first time at an iNACOL event and honestly, I thought it was one of the most impressive conferences I have ever attended.  There were more than 3000 attendees and over 200 workshops and presentations to choose from.  iNACOL is all about “personalized learning” and its annual conference is the industry’s leading event for K-12 competency-based, blended and online learning.  It was also amazing to see how many education leaders from NH were present and had prominent roles!

My one criticism of the conference was the lack of sessions that featured mathematics – especially since the request for proposals specifically asked for sessions that would focus on mathematics.  There were only one or two sessions that had a math focus and ours was one of them.  Our session was titled, Making the transition from a traditional teacher-centered mathematics classroom to a more student-centered classroom in a competency-based education model.  You can view our PowerPoint at

One thing I would like to share, which happened several times at the conference, is that whenever I am engaged in discussions that involve “personalized” or “student-centered” learning, there is often a reaction that math teachers and math departments are some of the most difficult groups to work with.  Many will say that they don’t engage and are lagging behind when it comes to transforming their practice.  Have you ever heard this before?

I will say that I am a little surprised by those who still insist on a strict dedication to a “traditional” approach to mathematics instruction.  I agree with Steve Leinwand when he says that traditional methods work well for about one third of your students.  If our mission is to reach ALL students, then a traditional approach alone falls disturbingly short.  In terms of making mathematics teaching and learning more student-centered, are we keeping up?

My trip to Pittsburgh was to visit Robomatter Inc.  Robomatter is the development and education division of Vex Robotics – which is a leader in educational robots. Vex Robotics “envisions a world where every student has the opportunity to be inspired by the excitement of hands-on STEM learning.”  Vex Robotics is also a course that is taught at many Career and Technology Education (CTE) Centers throughout the country.  I made the trip to Pittsburgh along with Nashua CTE Center Director Amanda Bastoni and head teacher Chris Knoetig.  We are working together thanks to a grant from the NH DoE devoted to “Improving Options for CTE Students in NH”.  Amanda is the leader and visionary behind the project.  We are looking into the feasibility of transforming Nashua’s current one-semester Vex Robotics course, taught by Chris, into a full-year course that would also include credit for Algebra 1.  Later, we will also be looking into the feasibility of doing something similar with their manufacturing course to include geometry.

Now, it may not be surprising that, while there are many who are excited by this project, there are those who won’t be.  I am keeping an open mind.  While I can see many challenges and have many questions, I am also intrigued and hopeful at the thought of finding MORE ways to make mathematics MORE accessible and meaningful to MORE students!

At Robomatter – and full disclosure, I know little to nothing about coding or robotics – I was definitely able to see opportunities where students could engage in some “real” mathematics that can also be aligned to CCSS-M – especially the 8 SMP’s – while using robots and technology as tools for learning.  With the use of numerous sensors and programs, robots can collect all kinds of data which can then be displayed, analyzed and altered.  Does this sound like a rich and relevant way to engage with mathematics?  Isn’t conceptual understanding of abstract ideas and procedures made stronger through the use of concrete experiences that can be modeled using mathematics?  Should this type of learning environment be limited to CTE students?  Can this experience be worthy of “mathematics credit”?  In terms of making mathematics teaching and learning more relevant, active, interesting, and fun, are we keeping up?

It really bothers me that so many people have a poor relationship with mathematics.  If we were to assign blame for this phenomenon, it would be widespread.  But I am not a fan of assigning blame.  Rather, I am advocating that, together, we continue to practice* and share ways to improve our instruction – to make it more student-centered.  Let’s also continue to explore more opportunities to make relevant connections such as those that exist in STEM or CTE.  In other words, let’s do our best to keep up!

I invite your feedback to my questions and comments.  I also welcome any support you can offer NHTM, as part of our mission to “improving the teaching and learning of mathematics so that each student is ensured quality mathematics education”.

*Using NCTM’s 8 Effective Mathematics Teaching Practices for example


Relationships + Growth Mindset = Middle School Math Success

By Daniel Pooler, Middle Level Representative

Being a middle school teacher, every year and, sometimes, every day is a new adventure.  You never know who will show up at your door.  Will they be eager to learn, or will they come in saying that they are “not good at math” because they are “not a math person”?  Will something occur outside of school or in another class that will shut them down to learning when you need them to be ready to learn?  How does one possibly prepare for all the obstacles and barriers that come up throughout the year to make sure all students in your classes are working to their potential every day?  In my experience as a middle school educator, the best solution I have found is to build strong relationships with your students, to provide a safe classroom environment for students to make mistakes, to provide engaging, real-world, problem-solving activities that force student struggle, and to always practice what you expect from your students.

Over the course of the past three years, my middle school has begun to focus on creating a transition period into each middle school grade that helps students get adjusted to new teams, new teachers, and new expectations.  Part of this change has included each grade using the Week of Inspirational Mathematics provided on by Jo Boaler.  Math teachers in 6th, 7th, and 8th grade classes start the year by going through the lessons with their students.  Each grade uses a different week to ensure no redundancy in materials for students.  The material takes students through engaging problem-solving activities that also allow the teacher to build classroom norms that support a safe environment.  I have found in the past three years that students are very engaged in the activities and the videos, which make it very easy to initiate classroom discussions around norms.

For me, the heart of my class discussions has centered around a few of Boaler’s Positive Norms to Encourage in Math Class.  Boaler’s first norm states that “everyone can learn math to the highest levels.”  Try selling this idea to any adolescent who is currently preoccupied by all the social, physical, and hormonal changes they are experiencing in their lives paired with their own history of math instruction and it most likely will go over like a lead balloon.  Combining this idea with Boaler’s second norm which states, “mistakes are valuable” and allowing yourself to share your own experiences with failure, makes the possibility of everyone being a math person more palatable for almost anyone.   I myself was never a “sports person” in school.  I share my experiences of not even wanting to try out for a sport for fear of not making the team with my classes, in hopes of drawing a parallel to their own fears about math.   I also share that I have changed my mindset about sports, so that I could become a softball coach for my own child.  The third of Boaler’s norms, that always starts conversations, is that in math “depth is much more important than speed.”  I find this is the key that opens the floodgates to students’ past experiences in math instruction.   This is again a place where sharing your own math experiences, good and bad, can build positive student relationships, foster a growth mindset, and establish a classroom culture where the eight math classroom practices can come alive.

Jo Boaler’s book Mathematical Mindsets (2016) and her Week of Inspirational Math has really changed the way I present mathematics to students.  I will absolutely admit that I had my doubts and fears about making the changes in my classroom that she suggests.  I also admit that I have made plenty of mistakes along the way and will continue to make mistakes.  The difference now is that I am no longer afraid of taking these risks and making errors because by using Boaler’s teaching in my class, I have begun seeing students’ mindsets change for the better about math and that is a win in my book.

As a special note, I look at this post as a first in a series that address how middle school teachers can build student mathematical confidence, change mathematical mindsets, and increase student mathematics understanding through the introduction of engaging, real-world problems and authentic learning activities that increase student critical thinking, communication, and collaboration.

Art’s Attic– Was Pythagoras a Druid?

By Art Johnson

The most famous equation in all of mathematics is the Pythagorean theorem: a2 + b2 = c2, where a and b are lengths of the legs of a right triangle and c is the length of the third side, the hypotenuse. You might make a case for E =mc2, but that is more a physics relationship and we are talking math here. Besides, the history of a2 +b2 = c2 is so much more interesting.

Did the Druids use the Pythagorean Theorem to build Stonehenge?

In a previous column I discussed Pythagoras and the cult of the Pythagoreans. Did Pythagoras himself discover the relationship named for him or was it some unnamed mathematician in the cult who dedicated the discovery to the revered founder? Nobody knows. One thing is sure. The Pythagorean theorem was known to the ancient Egyptians and Babylonians. But they did not apply it in all situations, only those where a, b, and c were all whole numbers, like a 3-4-5 triangle. Such side relationships are called Pythagorean triples. Some math historians have made the case for early peoples of the Americas having a form of the Pythagorean theorem, but only with the same Pythagorean triples.

Author and friend Frank Swetz found indisputable evidence (Was Pythagoras Chinese?, NCTM) that the Chinese had the full understanding of the Pythagorean theorem some 2500 years before Pythagoras. His discussion about how the theorem may have journeyed across Asia to the Eastern Mediterranean, where Pythagoras picked it up is less compelling. It is sure, however, that the Chinese beat Pythagoras to his theorem.

In a new book, Megalith (Wooden Books), Robin Heath suggests that the builders of Stonehenge in England used the Pythagorean theorem some 2,000 years before Pythagoras. He bases his claim on a number of right triangles that can be found within Stonehenge. For example, four major stones on site form a rectangle, whose diagonal forms two triangles with Pythagorean triples for side lengths. There are many other combinations of stones and burial holes that form right triangles.

Nearby Woodhenge, an early Stonehenge-like temple shows a 12-35-37 right triangle. A few miles west, the great stone circle at Avebury displays several right triangles. Stonehenge itself forms a right triangle with the site from which the bluestones for Stonehenge were cut, and Lundy Island, an important prehistorical site.

The evidence is interesting, if not compelling. Any three points on the site of Stonehenge will form a triangle. If you look at enough combinations of points, you are bound to come up with a few right triangles, including those that display Pythagorean triples. Nevertheless there are unusual triangle lengths at Stonehenge, and maybe the ancient builders were on to something. No one will ever know for sure, but it makes for interesting speculation, no?

DISCLAIMER: The Druids had nothing to do with building Stonehenge. It was just an easy way for me to grab a title for this column.

Seacoast Regional Group

The Seacoast Regional Group will be engaging in a book study this year, with the focus being NCTM’s “Catalyzing Change in High School Mathematics: Initiating Critical Conversations”.  The first meeting will be on Monday, October 15th, with three subsequent meeting dates to be determined later.  All meetings will be at Exeter High School from 4-6 pm.  For additional information, contact Michelle Morton-Curit at



Update from the Membership Chair

By Bernadette Kuhn

NHTM continues to offer free one-year NHTM memberships to undergraduate students, pre-service teachers, first year teachers, PreK-6 teachers who have not held a NHTM membership previously, and experienced teachers in their first year of teaching within New Hampshire. The free one-year membership will also make the member eligible to receive the “reduced rate” at the NHTM Dine & Discuss and Fall Conference (which typically is set just high enough to cover meals) for that membership year. Proof of eligibility for the membership will need to be shared with the membership chair, via email or USPS, by the applicant prior to receiving any membership benefits. Please send proof of eligibility to Bernadette Kuhn at, or mail to: Bernadette Kuhn, NHTM Membership Chair, 145 Eastern Ave, Keene, NH 03431-4358.

Please RENEW & Invite Colleagues to Join NHTM

 Now is the time to renew!

We hope to see you at the Fall ATMNE conference on December 6-7 in Rhode Island. You will need a current NHTM membership to register for the Fall ATMNE conference. You can use your email address to log into our website, to check the status of your NHTM membership. Reminders have been emailed to all members for the upcoming academic year. (If you have not received a reminder, or you would like to join NHTM, contact me at the email address below.) Let NHTM be your state level professional conduit that extends your networking with mathematics colleagues. Enhance your effectiveness, mathematical expertise, and teaching skills. This is the perfect time of year to invite a colleague to join NHTM, especially if you know someone who would qualify for a free one-year membership to NHTM. Contact Bernadette Kuhn, Membership Chair, if you have any further questions:

Individual Membership in NHTM provides you with:

  • Mathesis (newsletter) – includes current happenings in math education, Common Core resources, interesting articles and math activities
  • Reduced rates at NHTM sponsored events
  • Membership in ATMNE (the Association of Teachers of Mathematics in New England) including its two publications, the ATMNE Newsletter and the New England Mathematics Journal, and reduced rates at ATMNE conferences. Note that the ATMNE Newsletter has gone GREEN – be sure your email is up to date in our database.
  • In-Service Education Forums on current Math Ed initiatives – Regional PD offerings, networking

What Your Membership Supports:

  • Scholarship programs for graduating high school seniors who will pursue mathematics related college studies and for college students enrolled in mathematics education programs
  • State Mathematics Contest for high school students and MATHCOUNTS for middle school students in New Hampshire
  • Student Recognition program – for students who have demonstrated creativity, interest, or talent in the study of mathematics
  • Mathematics Educator Recognition Programs:
    • Richard H. Balomenos Memorial Service Award
    • Presidential Awardees (PAESMT) at the elementary and secondary levels
    • Fernand J. Prevost Mathematics Teaching Award  for outstanding teacher of mathematics in their first, second, or third year of teaching
    • Richard C. Evans Distinguished Mathematics Educator Award for distinguished mathematics teacher/educator who works actively with students and/or teachers for five or more years at any level (PreK-16)
    • Recognition of NHTM math educators with 25 or more years of NHTM membership
    • Lifetime Honorary Memberships

Please continue to explore our website at  throughout the school year for updated membership information, mathematical resources, and professional development opportunities.


Vote for Beverly Ferrucci– Candidate for NCTM Board of Directors

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Beverly is a Professor of Mathematics at Keene State College and Director of its Elementary School Teachers Mathematics Program. She has been active on the state, regional, and national levels. Beverly served as an NHTM President, an ATMNE Representative for NHTM, and as an NHTM Conference Chairperson multiple times. She is the editor of the New England Mathematics Journal and has served on the ATMNE Board as President, Newsletter Editor, Web Master, and Conference Chairperson. Her work for NCTM includes being Chair of the Educational Materials Committee and the Partnerships in Research Committee, along with serving on NCTM’s Research Advisory Committee and Conference Program Committees.

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Secondary Representative– Are Norms the Norm at Your School?

By Lesley Fallu

If you move from one math classroom at your school to the next and the next, what do you see? Are the expectations different from one teacher to another? Or, are the teachers working as a team with a common set of norms?

The President’s Message on the NCTM website this month is titled “Positioning Students as Mathematically Competent.” Robert Q. Berry, III, concludes his message urging that this positioning “must happen with clarity and consistency” and suggests 5 questions for each of us to consider:

  • How do I create classroom norms and routines that support students to take risks to engage in mathematical discourse?
  • In what ways are students’ mathematical ideas shared and valued?
  • How do my teaching practices communicate to each and every student that their ideas matter?
  • In what ways is intellectual authority distributed in my classroom?
  • How do my teaching practices use students’ ideas to guide them to important mathematical insights and understandings?

My focus is on the first of his questions, creating norms for the math classroom. I believe that if the norms are developed and used daily, that the answers to the remaining questions will be apparent.

To get started, Jo Boaler, Professor of Mathematics Education at the Stanford Graduate School of Education, suggests 7 norms in “Setting up Positive Norms in a Math Class.” Creating these norms with healthy discussions in the classroom ensures that everyone has a common understanding. These are the 7 norms that she cites:

  • Everyone can learn math to the highest levels.
  • Mistakes are valuable.
  • Questions are really important.
  • Math is about creativity and making sense.
  • Depth is more important than speed.
  • Math class is about learning not performing.
  • Math is about connections and communicating.

There is no doubt that each of us has a similar set of norms which guides our students, and hopefully positions them for success, but are the norms for your classes consistent with those of other teachers in your school? I’d like to take a step back with this norm development process. Before addressing this in the classroom, let’s address it with our colleagues. Can we develop a common set of norms to support our students? Imagine the impact on our students if, from year to year, they had this consistency. The students in my classes this year, may be your students next year.

This is a perfect time for reflection as we prepare for a new school year. Challenging all of our students to learn mathematics may begin with the norms we set. Have you created a set of successful norms? If so, please share your thoughts.

News from NCTM: Exemplary Resources for Teaching Mathematics


By Terri Magnus, NCTM Representative

The question has been posed:  Why are professional organizations such as NCTM and NHTM important in a world where we can access information and network on the internet?  Your New Hampshire Teachers of Mathematics Board is eager to hear how we can be more relevant and play an important role for mathematics teachers in New Hampshire.  Please contact any one of us with your suggestions.

As the premier mathematics education organization in the United States, the National Council of Teachers of Mathematics plays an essential role in linking recognized research in mathematics education to best practices in teaching.  It is your voice in Washington, D.C., advocating politically for national policies that will encourage, enable, and empower teachers to put best practices into action in their classroom.

Yes, you can find a variety of mathematics lessons on the web, but not all of them are properly vetted.  Do the lessons encourage mathematical thinking? Are they accessible to all students? Do they properly prepare students for the mathematical understanding they’ll need in future courses?  Are you as a teacher able to view your lessons and your entire course in the context of the broader education your students will experience and the needs they will have upon completing their formal education?  Math education trends and popular curricula may come and go, but NCTM’s Principles and Standards have stood the test of time, being reinforced and clarified as more research has taken place.  New research into equity, access, and empowerment builds upon and complements the Principles and Standards.

As an NCTM member, you can access journals with lesson plans and articles that have been approved by an editorial team. You can participate in a social network that revolves around the needs of mathematics teachers—and possibly get a response from a current or former NCTM president or board member.  Members get access to classroom resources such as Illuminations, Figure This!, Calculation Nation, and Problem of the Day. Members get access to the grade-level publication of their choice and discounts on NCTM books and conferences.  There are also grants you can apply for to help you accomplish the goals you have!

This October 4-6, NCTM is coming to Hartford, CT!  Take advantage of the opportunity to participate in workshops and talks that will energize your teaching. There is something special about attending a regional or national NCTM conference that gets you thinking about your teaching in new, effective, and achievable ways. Register at  The early-bird deadline is September 12.

New releases at theNCTM Bookstore include:


President’s Message– On a Mission

By Rob Lukasiak

I am humbled and excited to be writing my first message as NHTM president.  To help guide me in my new role, I have been focusing on NHTM’s mission statement.  In fact, I shared this focus with my fellow board members at our summer retreat where I asked them to reflect on the statement and think about how well we are aligned to it.  Now, I would like to ask YOU to do the same – and hopefully, if we are using a new format for the newsletter, you may even be able to post your comments directly to this message!

Here is our mission statement:

The mission of the New Hampshire Teachers of Mathematics is to provide vision and leadership in improving the teaching and learning of mathematics so that each student is ensured quality mathematics education and each teacher of mathematics is ensured the opportunity to grow professionally.

I will get the conversation started by sharing some of my own observations.  First, I’m hoping that you agree that the mission statement is meant for all NHTM members.  As a result, providing vision and leadership toward fulfilling this mission is our collective responsibility.

Next, while I can’t guarantee that we all have the same vision, I can at least tell you that my vision includes classrooms where students are clearly demonstrating characteristics of the 8 Standards for Mathematical Practice (SMP’s) and teachers are demonstrating characteristics of the 8 Mathematics Teaching Practices (MTP’s).  My vision also includes a professional organization that is vibrant with interactions among its members where ideas, challenges, and resources are regularly exchanged.

Then I wonder how well are we doing in terms of reaching each student and each teacher?  Of course, this part of the mission statement is addressing the issue of equity.  I’m sure we all know how prominent and divisive this issue has been in NH over the years, yet it continues to be a serious problem.  It should not be the case that the quality of a student’s mathematics education is a function of the track they are placed in, inequitable teacher assignments, or their zip code.  Further, all teachers need access to quality resources, professional development, and collaboration even if their district lacks funding or if they live in a remote location.

I am proud to be a member of NHTM and to support our many efforts to improve mathematics education in NH, but we can do better – especially when it comes to how we connect and communicate as an organization.  For one thing, our current newsletter format is ineffective and outdated.  While a great deal of time and effort goes into creating the newsletter, we know that very few people actually read it!  These days, a quarterly, one-directional communication tool cannot compete with “interactive”, “real time”, social media formats like Facebook and Twitter.  Needless to say, we need to modernize, especially if we expect to reach more teachers and to attract new members.

So, I guess you could say that I am on a mission – to improve our ability to connect and rely on each other – to strengthen and widen our professional community.  A modernization and expansion of our communication tools is necessary for this to happen.   I invite you to share your ideas and experiences to help us move forward in this area.  Let’s work together to reach more teachers – physically, virtually, or otherwise, so we can ultimately improve the mathematics learning experience for each and every student in NH!

The Journey Begins– The New NHTM Blog!

By Elisabeth Johnston– NHTM Newsletter Editor

This year we decided to try on new format for the Mathesis. We want to connect in different ways with NHTM members and mathematics teachers across the state of New Hampshire. Unlike the traditional Mathesis, content will be published on a weekly or bi-monthly basis instead of once each quarter. This new blog is a pilot and we welcome feedback about the format as well as suggestions for content.

Enjoy! Best wishes for a successful school year!