#INspirEDmath

August 2019, Volume 12

Increasing Number Sense - Every Grade, Every Day

One in five U.S. adults lacks the math competency of a middle school student (Neergaard, 2013). This is not just "school" math but relevant, useful, daily math such as figuring out the tip on a restaurant bill or scaling a recipe with fractional measurements up or down. Improving our students' number sense is not only the responsibility of our elementary teachers, but of all teachers kindergarten through calculus. Implementing instructional routines focusing on number sense daily is a must, and really quite simple! Read on for resources, strategies, and tips to help your students make sense of numbers!
Math class needs a makeover - Dan Meyer

Problem of the Month

Secondary Problem of the Month

Do your students need more opportunities do develop number sense and reasoning? Give it to them through daily number sense routines!

Find Order Me On a Number Line and many more strategies in Daily Routines to Jump-Start Math Class, High School: Engage Students, Improve Number Sense, and Practice Reasoning by Eric Milou and John J. SanGiovanni.

Elementary Problem of the Month!

Where's the Point? This routine help students:
  • Reason about number relationships
  • Develop ideas about benchmark relationships
  • Build number sense
  • Think flexibly about quantities
  • Reason about the closeness of values
  • Defend their reasoning
Find this routine online at the Corwin Publishing Company and other Daily Routines to Jump-Start Math Class in this book by John J. SanGiovanni.

What is Number Sense (Numerical Fluency)?

Number sense, also known as numerical fluency, can be described as being fluid and flexible with numbers. According to Kanter and Leinwand, “Fluency is not a simple idea. Being fluent means that students are able to choose flexibly among methods and strategies to solve contextual and mathematical problems, they understand and are able to explain their approaches, and they are able to produce accurate answers efficiently." (Developing Numerical Fluency, p. ix)


The National Council of Teachers (USA, 1989) identified five components that characterize number sense: number meaning, number relationships, number magnitude, operations involving numbers, and referents for numbers and quantities. These skills are considered important because they contribute to general intuitions about numbers and lay the foundation for more advanced skills.

Researchers have linked good number sense with skills observed in students proficient in the following mathematical activities:

  • Mental calculation (Hope & Sherrill, 1987; Trafton, 1992);
  • Computational estimation (for example; Bobis, 1991; Case & Sowder, 1990);
  • Judging the relative magnitude of numbers (Sowder, 1988);
  • Recognising part-whole relationships and place value concepts (Fischer, 1990; Ross, 1989) and;
  • Problem solving (Cobb et.al., 1991).

Supporting Numerical Fluency Every Grade, Every Day

Number sense develops over time. It is not a chapter in a textbook, or a unit in a curriculum. It is not something that you teach the steps to and move on. Numerical fluency builds from initial exploration and discussion of number concepts to using informal reasoning strategies based on meaning and properties of the operations.” (Developing Numerical Fluency, p. ix) Students develop number sense gradually through the exploration of numbers, visualization, through context, and relating numbers in a variety of ways. Here are a few research-based strategies to build number sense in any grade:
  • Model various methods for computation
  • Ask students to calculate mentally
  • Have students share their strategies for computing
  • Make estimation a must when computing
  • Ask students about their reasoning - both when they make mistakes and when they are correct
  • Ask questions with more than one possible answer

For more information on each strategy, click here.

Article - Why is Number Sense Important - A MUST READ!

All The Mathematical Methods I Learned In My University Math Degree Became Obsolete In My Lifetime by Keith Devlin, Contributor and mathematician at Stanford University in Palo Alto, California.

Opportunities For The Field

Mathapalooza - An Extraordinary Event!

Increasing engagement in the K-12 math classroom through FREE full-day math-specific professional development and YOU are invited!


Indiana Department of Education’s (IDOE) math specialists from the Office of School Improvement are organizing another professional development series to continue our support of a vision for ambitious instruction in the K-12 math classroom! Participants will explore and develop rich tasks that support the Eight Mathematics Teaching Practices as outlined in NCTM’s publication Principles to Action (2014). In this interactive and engaging full day session, participants will discover how to open up traditionally closed problems to promote student discourse, provide opportunities for productive struggle, and to support students in risk-taking and sense-making. Guided implementation and opportunities for collaboration will be embedded throughout the day. Classroom teachers and coaches are the target audience, although the support of building level administrators is highly encouraged!


Details:

  • Five PGP’s will be given for educators who attend the full day professional development

  • Educators should bring a laptop or other device

  • Each site will have the following schedule, with minor variations in time, dependent upon location: 8:30am – 2:30pm with a 1-hour lunch on your own

  • Space is limited to 150 educators (75 secondary and 75 elementary) at each location so sign up quickly to reserve your seat!

  • Registration Link

NEST ICTM Project - New Educators Succeeding Through Indiana Council of Teachers of Mathematics

The NEST ICTM project is a unique, induction program to retain high quality beginning mathematics teachers in Indiana. The NEST ICTM project focuses on two of NCTM’s strategic priorities:

1. Teaching and Learning: The NEST ICTM project attempts to support beginning teachers in their first years in the classroom. We will provide beginning teachers with access to professional support for the planning and implementation of high-quality, equitable mathematics instruction.

2. Building Member Value: Creating this community of dialogue and professional support among veteran and new teachers will be mutually beneficial, as resources are shared and all are committed to improving their practice toward equity. With your help, we aim to attract and support other new teachers to next year’s conference, and perhaps advocate for others in their school district to join ICTM and NCTM.

Eight teachers will be selected to attend the 2019 ICTM Fall Conference on September 29-30, 2019 for FREE. The conference theme is Math Teachers as Transformers: Transforming Learning, Transforming Lives. Benefits include:

● Free conference registration, Monday luncheon included

● One-night stay at Marriott East, paid for by ICTM

● Substitute teacher payment reimbursed

● Free NCTM Essential Membership for one year

● $50 gift certificate to NCTM’s Bookstore

Required Commitments for NEST ICTM participants:

● Attend 2019 ICTM Fall Conference sessions on both days, including “Celebrate Your Journey: Thriving in the Teaching Profession” and “ICTM 101: What you need to know to have a great first conference.”

● Share your conference experience at the February 2020 ICTM Board meeting.

● Assist in planning the 2020 ICTM Conference and the NEST ICTM experience.

● Present on your professional experience at ICTM 2020 Conference or NCTM Regional, or write about it in ICTM’s Mathematics Teacher Journal.

Apply now! Copy & paste: https://tinyurl.com/yxa7qu5b

Questions? Contact: Jean Lee, jslee@uindy.edu
NEW! Advanced Placement Curriculum and Resources

Thousands of released AP questions, customizable practice tests, progress dashboards, pacing and sequencing suggestions, strength and weakness guidance, and more! Teachers, the deadline has been extended for this FREE binder, a $300 value.

Who To Follow On Twitter

Math Educator Spotlight - Ryan Dubovich

Nominated by: Ellen Volz

Why he is awesome: "He makes learning fun and challenges students at the same time. He is very passionate about what he does."


I was born and raised in Hobart, IN. My mother was an elementary school teacher and my father owned his own business. I attended Indiana University and received a degree in marketing through the Kelley School of Business. After an early career in retail management that wasn’t very rewarding, I gathered the courage to leave that profession and go back to school to become a teacher. After attending Ball State University, I received my license and masters and was hired by Westfield. I was encouraged and supported by my wife, Jodi, who was an elementary school teacher (now instructional coach). We live in Westfield with our five year old daughter, Autumn.

I have had the privilege and honor of teaching students at Westfield Intermediate school for 10 years. During this time, I taught a variety of subjects and grades five and six, including math, social studies, and science. The majority of my time in education has been spent teaching several levels of math. While this profession can be challenging and tiring, it is also one of the most rewarding.

Throughout the years I have experienced students of many levels and abilities. The one constant that I see is that students need to be taught and shown the soft skills to succeed, such as having positive self-esteem and confidence in their abilities. This is my overriding goal when working with students at this age. Math should be seen as a fun challenge that can have real world implications for students now and when they enter the world as adults. Once they see the value and purpose in what they are learning, I feel that they are more motivated to reach the untapped potential that exists in all of them.

Mathematics Educator Spotlight Nomination

We are looking for rock star math educators who are innovative and inspiring; educators who lead, learn, and collaborate with humility and passion. If you know someone (or are that someone) click the button and nominate them (or yourself)!

Your IDOE Mathematics Team