Welcome!

Welcome to the NEW Vermont Council of Teachers of Math eNewsletter!  We are proud to offer this newsletter to all math teachers in Vermont as a way of creating a better math community.  We will bring you the news of the region- from the VCTM and the New England association of math teachers (ATMNE), as well as the national NCTM.  Based on your needs, we will design conferences and provide the information you need to attend them.  Additionally, this blog site will provide links to different resources for your classroom, create discussions amongst colleagues around the state, and be receptive to your queries and quandaries.

So let us know of your needs as Vermont moves to the Common Core.  Tell us strategies that work in your classroom.  

December 2013 VCTM Newsletter

In this December 2013 Issue:

• President's Message- Jason Cushner
• Mahesh Sharma Interview
• Common Core lesson resources
• A paper on math coaching to help others teach deeper
• Algebra for All- but when?  The president of the NCTM chimes in.
• New Study Finds That Gender is NOT a Predictor of Success on Math Tests
• Smarter Balanced test resource
• ATMNE Conference in Killington:  Where the Elite. Met (wow, that lost its rhyme in the past tense, didn't it?)
• Ken Gross- More than 12 Dozen Accolades to the Bezuska Lifetime Service Award for Teaching and Learning

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President's Message    December 2013

I hope you are all doing well during this intense time of year.  It was wonderful to see so many of you at the ATMNE Fall Conference.  Just after that VCTM held a retreat to create a vision for the next couple of years.  We are an organization that is committed to students having a math education that is engaging and prepares students for the future.  Some schools are still operating in an education system that is outdated, and we need to prepare students for a rapidly changing world while we get ready for the Common Core State Standards and Education Quality Standards that are coming our way.

VCTM has chosen three main projects to take on this year to support in that effort:

1. Creating a digital platform that provides support and connections for what you need in math education

2. Start a local learning series to provide professional development and connections in your region

3. Creating the next VCTM conference that provides a window into what’s happening statewide with the implementation of some of the new and evolving math education practices

We welcome  your feedback on how VCTM can best serve math education in Vermont.

Jason Cushner

VCTM President

Program Coordinator Big Picture South Burlington

Rowland Fellow

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Mahesh Sharma On Common Core, Flipping the Classroom, and Non-Negotiable Skills:  I recently had the opportunity to sit down and talk with math education expert, Mahesh Sharma.  Having the good fortune to have taken his class when it was offered at St. Michael's 23 years ago, I reached out to him to offer his thoughts about the Common Core and other subjects when he was in Montpelier last week doing teacher training for several school districts.  To read the interview, scroll below to the next post -  David Rome

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You've Got to See it to Believe It! If you're like me, figuring out how to teach lessons that you have been using in the past being mindful of  the Common Core can be a daunting challenge- VCTM Board Member  T.J. Jemison recommends this Illustrative Mathematics site to help you find lessons and activities that get at the deep instruction needed to meet CCSS standards

Using our neighbors to the west, we can learn much more about the Common Core through their Engage NY website.  So many articles and videos- take advantage of the fact that there are are many available lessons and ideas for you to pluck off the ones that you need.

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K-5 Coaching- New Opportunities With New Approaches  While the focus of Board member Tracy Watterson's paper is about the transformation of an elementary school teacher's transformation via a math coach, all can benefit from reading about the process.  A new organization in Vermont, the Vermont Math Leadership Council, is there to find new leaders who are invigorated by stories like this.  ​

 Reflections of a Coaching Task Revisited.doc

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Algebra:  Not If but When by NCTM President Linda M. Gojak
One of the questions I am asked frequently by teachers, parents, and reporters is, “When should students take algebra?” Let’s assume that we’re talking about a college preparatory algebra 1 course. The content and instruction must be designed to develop both conceptual and procedural understanding. For students to be considered successful in first-year algebra, the expectation must be that reasoning and making sense will be priorities of both teaching and learning. Read more.

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Remediation, Not Gender, Plays Role in Increasing Test Scores.   A Geogia (state) study has found that gender differences on standardized test scores are insignificant, something that most of us have felt was a decades old stale notion.  What the study does show, however, is that remediation is effective for raising test scores.  While the study is long and will likely eat a half ream of paper if you choose to print it out, the implications section begins on page 72 and has some interesting observations- thanks to Carole LaVigne of Burlington HS for finding this for us.

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No- It's Not a Breakfast Cereal.  But we will be having it served up soon- so you can get a preview of the menu of the NECAP replacement, the  Smarter Balanced test.  It's coming folks- so if you would like to stay current about the test that will replace the NECAP in 2014-2015, then please use this resource.  

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ATMNE Conference in Killington- More than 350 math educators from all around New England met in October in Killington.  Past President sends us her photos and description of the conference in case you missed it!  ​

 Killington intro.docx

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 Balomenos and Father B Awards.docx

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Ken Gross- A Man for all Teachings.  For those of you who know him or have been taught by him, there is no doubt that Ken Gross of UVM, the recipient of the of the Rev. Stanley J. Bezuska Lifetime Service Award for Teaching and Learning was deserving.  A humble and humorous man, he has engaged thousands of UVM students and summer high school students at the Summer Institute every summer.  Ken was honored at the October ATMNE conference held at Killington, and for more about Ken's accomplishments, read more about them here.

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Mahesh Sharma Interview

I recently had the opportunity to sit down and talk with math education expert, Mahesh Sharma.  Having the good fortune to have taken his class when it was offered at St. Michael's 23 years ago, I reached out to him to offer his thoughts about the Common Core and other subjects when he was in Montpelier doing teacher training for several school districts recently.  The following is an excerpt of our conversation.  -  David Rome

DR:  Many teachers are going toward the Core Curriculum State Standards in Math (CCSSM) a little bit skeptical- wondering how is this going to be any different from the standards we had in the past?

Mahesh:  The main difference between these standards and most of the previous state standards and frameworks is that the CCSSM are mathematically sound- they have focus, rigor, and coherence.  They are aimed at helping develop student’s mathematical way of thinking.  They should serve as the foundation for creating proper school math textbooks, better teacher preparation, effective lessons and meaningful student engagement and higher achievement and interest in mathematics.  When teachers understand the intent and content of these standards, align their curriculum with CCSSM expectations and convert them into daily lesson plans coupled with appropriate progress monitoring, then children’s mathematics achievement will rise.

DR: Why do you feel that some teachers are resistant to the changes? 

Mahesh:  The standards call for examining how teachers teach and how and what students, at each grade level, learn, know and communicate the mathematics they know, not what is covered.  CCSSM are demanding and is not business as usual.  For students to learn the standards well, we need to teach them with understanding, fluency and applications.  We need to convey the mathematician’s art; asking simple questions.  This will take a lot of planning and introspection to our pedagogy. The standards call for our own understanding of mathematics and its structure.

DR:  How does CCSSM differ at the elementary level from middle and high school?

Mahesh:  The focus of math content in the CCSSM in the elementary grades is on mastering key arithmetic concepts and procedures with deeper understanding so that the students are prepared for more demanding mathematics in middle and high school and beyond.  Such a focus means mastering certain non-negotiable skills at each grade level. 

DR:  Non-negotiable skills?  Such as….

Mahesh: Students know number concept at the end of Kindergarten, addition facts by the end of first grade, additive reasoning by the end of second grade, multiplication by the end of third grade, and division by the end of fourth grade.  This means students should master number concept, number sense and numeracy.  Numeracy means a student’s ability to execute whole number operations correctly, consistently, fluency in standard form and understanding by the end of fourth grade.  Then, students can learn mathematics better.  Another example, fractions- the concept is introduced, in CCSSM, earlier in the third or fourth grade, first by using the same denominator, but by fifth grade, children have mastered the operations on fractions with deeper understanding.  Similarly, multiplication is introduced in the second grade as repeated addition, equal groups of objects, and arrays.  By the end of third grade, however, children should have mastered the concept as repeated addition, groups of arrays, the area of a rectangle so they understand the distributive property of multiplication over addition and subtraction, have automatized multiplication facts, and are prepared to multiply fractions in fifth grade using the area model of multiplication then apply multiplication of fractions to master the operations of addition and subtraction on fractions with efficiency and understanding.  By the end of sixth grade they have mastered operations on whole numbers, fractions (parts-to-whole, comparison of quantities, decimals, percent, ratio, proportion, scale factor, etc.) and integers. 

DR:  What about students who understand how to multiply earlier than the others- is it fair to hold them in the same classroom than those who are just learning the concept?

Mahesh:  A student may be able to do a procedure, but not fully understand the concept behind it so when it comes time to use this concept in a different way, they are no longer that ‘gifted’ student they were in earlier grades.  With a focus of mastery of non-negotiable skills, the teacher can pay attention to children’s errors, misconceptions, or lack of mastery in proper time.  At present, we devote a great deal of time on preview, pre-testing, and our classrooms have become so diverse in mastery and preparation.  Teachers find meeting individual needs to be very difficult.  They have multiple preparations for the same class with only coverage as a focus, rather than mastery. While many parents would differ in this notion, there are very few ‘gifted’ students who are just that; where they understand the procedure earlier, as well as the concept.  Procedure without concept is a recipe that cannot work later on in their math learning.  There are some gifted children in every classroom, but  their needs must be met, first by deepening their understanding, broadening their conceptual schemas, and increasing their fluency in all aspects of mathematics- linguistic, conceptual, procedural, and skills.  Narrow acceleration of procedures for these children takes them to a situation that they “burn out”- they plateau in their reach, or simply memorize and apply mindless procedures on sheets after sheets.  They need to engage in mathematics conversation, have a chance to present their thinking about a problem, critique others’ reasoning, make connections and apply their knowledge in meaningful problem solving alone and with others.  A truly gifted child (who has master of linguistic, conceptual, procedural and efficient skills) needs to be with his peers of similar thinking- in an accelerated (honors) program with a competent teacher who knows mathematics.  This means vertical acceleration.

DR:  How do you feel about the concept of a ‘flipped’ classroom where students watch a lesson on-line and then do their practice in school under the guidance of a teacher?

Mahesh:  First off, the quality of the videos available to students is poor.  The largest outlet, Khan Academy, teaches only procedural methods without the development of any conceptual schemas.  He teaches how to solve a problem, but not how to think about it, why does that procedure work, what are the relations of that particular procedure to other math concepts.  They are very good when a competent teacher has introduced the topic and related the concept, developed the linguistic and conceptual schemas for the mathematical idea.  Teaching is about having a discussion; discussing all the possibilities.  Students have no interest in the concept if they have been introduced to the procedure first.   Changing one’s pedagogy to a flipped classroom is simply ‘rearranging the chairs on the Titanic.’  A teaching lesson has four components:  linguistic, conceptual, procedural, and skill.  The first two require conversation rather than lecture.  A video simply cannot provide what a teacher can deliver.  A teacher has three roles: didactic, Socratic, and coaching.  The videos, books, collecting information from the internet, etc. are didactic components of teaching.  They provide information.  This information needs to be converted into knowledge—language of mathematics, conceptual schemas, and skills.  This conversion takes place by discussion, by exchange of ideas, messing around with methods and information, guided discovery, etc.  The role of the teacher is to pose problems, ask questions, scaffold their thinking, provide examples and counter examples, refute their findings, provide encouragement as they wrestle with ideas.  It is not just practice exercises after watching a video.  It is developing mathematical way of thinking—discerning patterns, extending patterns, creating patterns and applying patterns.  Teacher’s role is not just to supervise practice.  Moreover, CCSSM suggests certain mathematics instructional practices (they are 8 of them) videos do not involve even two of them. They are wonderful for some students, but not for all students. If you want to use them (judiciously selected), use them after you have introduced the language, conepts and the procedural idea in the class.  They will be wonderful as practice tools and reinforcement.  Your classroom should be augmented by going to them not before your introduction of the idea. We need to use these available resources, but not usurp your role (didactic, Socratic, and coaching) as a teacher.  They should be in the mix of all of the resources you as an effective teacher should use.

Mahesh Sharma is the former President and Professor of Mathematics Education at Cambridge College where he taught mathematics and mathematics education for more than thirty-five years to undergraduate and graduate students. He is internationally known for his groundbreaking work in mathematics learning problems and education, particularly dyscalculia and other specific learning disabilities in mathematics.  Mahesh is an author, teacher, teacher-trainer, researcher, consultant to public and private schools, and a public lecturer. He was the Chief Editor and Publisher of Focus on Learning Problems in Mathematics, an international, interdisciplinary research mathematics journal with readership in more than 90 countries, and the Editor of The Math Notebook, a practical source of information for parents and teachers devoted to improving teaching and learning for all children.

Do you have questions you would like Mahesh to answer regarding techniques that would enhance your teaching using the Common Core?  Post them below, and he will respond on this blog.