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Philosophy

NLSI Philosophy


No one would deny that education is vitally important to the future economic and political success of any country. Mathematics is the subject that will be at the foundation of all new discoveries, especially in the areas of medicine, renewable energy and transportation technology. Yet, we are at a crossroads and now face the complex challenge of improving our education system. One facet of this improvement has to be in the area of mathematics education. There are many different voices calling for mathematics reform. Where do we look for a solution? Is it in the curriculum, assessment, or in the classroom?

There is no one right answer but we have come far enough to realize that teachers hold the key to improving student learning. Such a simple and obvious statement belies the importance and complexity of improving the teaching of mathematics.

Teachers tell us that they are ill prepared to deal with the challenges of teaching mathematics when they graduate from their college or university program. This is especially true of elementary teachers who usually enter the teaching profession with very little background knowledge in mathematics and how to teach it. Teachers face classrooms every day with students who have a wide range of ability levels, diverse learning styles, a wide range of literacy skills, and a lack of intrinsic motivation. These challenges can be overwhelming to new and experienced teachers alike so, how do we prepare teachers to know and understand the mathematics needed to teach effectively?

We know from a large body of research in mathematics education and through our many years of working with teachers in the classroom that improving a teacher’s capacity to teach mathematics must include the following components:

Teachers need to learn how to unpack familiar mathematical concepts into those elements that combine and lead to an understanding of the concept.

Knowledge of what is an adequate explanation of a concept or justification of a procedure.

An understanding and exploration of solutions or methods that is different from their own.

This type of ‘on-the-job learning’ can only take place with a supportive school leadership team, excellent teaching resources and a professional learning community within the school.

Strategy

NLSI Strategy


Neufeld Learning Systems Inc. (NLSI) combines the excellence of The Understanding Math Series of programs and our Professional Learning Series (PLS) to improve a teacher’s capacity in the instruction of mathematics. The Understanding Math programs “unpack” the mathematical concepts into their discrete sub concepts. These concepts are developed from the concrete to the pictorial to the abstract using multiple representations. This approach makes mathematical concepts accessible to everyone. The Understanding Math Series of programs combines a highly interactive computer based learning environment that enables students to learn from their mistakes and at their own pace.

Our PLS provides a series of leveled workshops that lead participants to further develop their instructional capacity for mathematics. The workshops give teachers the theory and practicality of effective implementation strategies. The focus is on integrating a variety of resources – technology, instructional strategies, manipulatives, textbook, etc. – into their mathematics program. This approach lays the foundation for a program that gives each student the opportunity to make connections in an inquiry based, student centered learning environment.

There are 3 levels of professional development workshops in our PLS:

  • Level 100: The first workshop of the PLS is focused primarily on modeling and supporting efficient use of the software. The more specific goals of the workshop are for the participants to be able to understand and discuss the 6 grounding principles of NLSI; moving from the concrete to the pictorial to the abstract, multiple representations of concepts, interactivity, learning from mistakes, pacing controlled by the learner and, using a wide variety of teaching strategies.

  • Level 200: The main focus of the second workshop is on implementation strategies for Understanding Math and Understanding Numeration in the classroom. In the level 200 workshop, participants will; understand different classroom and group structures for integrating the software, have opportunities to explore the theory and supporting research and apply this knowledge to the classroom, develop an assessment task and rubric to evaluate student learning, and plan a unit using the Understanding Math programs and other classroom resources.

If improvement is sought in student performance on standardized tests then there must be focused attention on affecting what happens in the classroom while teaching students mathematics. Change has to be connected to changes in teaching. Teachers, like students, learn best by doing, reflecting, exploring, proving, additional practice and the process repeats.

Ideally, the workshops would be organized for early in the school year (first third) so that there is carryover from the workshops into their classrooms. Our Math System Specialists work closely with district leadership teams to support the smooth integration of The Understanding Math System into the district’s professional development framework.

“Any successful reform initiatives have to affect change at the instructional level, in the classroom.”

-Michael Fullan, 2006

Features

Understanding Math - Features


The Understanding Math Series of programs consists of 10 distinct programs.

Understanding Numeration is designed for Kindergarten to 3rd grade. Five key concepts within numeration are addressed; counting, operations, comparing and ordering, place value and problem solving.

Understanding Math is designed for the 4th to 10th grade levels. There are nine programs within Understanding Math: Algebra, Equations, Exponents, Fractions, Graphing, Measurement and Geometry, Percent, Probability and Whole Numbers and Integers.

  • Understanding Numeration contains English and Spanish auditory enhancements along with text support
  • Understanding Numeration contains tests based on skills presented within each level
  • In Understanding Math all sections within each program contain practice questions and topic tests with randomly generated questions
  • All programs are highly interactive with graphical step-by-step explanations

  • Mathematics concepts are developed from the concrete to the pictorial to the abstract
  • Concepts are developed using a variety of representations
  • Mistakes are opportunities to learn and build confidence, therefore hints are offered to the student to help them form their own understandings
    • Extensive collection of resources available at www.neufeldmath.com
    • (e.g. correlations to state mathematics curriculum standards, support sheets, word banks and, Understanding Math Program Explorer)
  • NLSI is committed to continuous improvement to ensure that The Understanding Math System remains on the cutting edge of technology-based solutions and support for educational excellence in mathematics. Customer input is critical to our continuous improvement process. This feedback has led to significant enhancements in our soon to be released web based version of Understanding Math (i.e. student tracking and management system, audio capabilities, and test customization).
Benefits

Understanding Math - Benefits


  • Improve student understanding of mathematics concepts through the use of concrete and pictorial representation through a variety of approaches
  • Provide teachers with learning opportunities to deepen their understanding of mathematics. The Understanding Math Series of programs “unpack” mathematics ideas and procedures into discrete sub concepts
  • Provide teachers with a broad range of implementation strategies to reach students of all learning styles and ability levels
  • Provide schools with a focal point for developing professional learning communities and therefore a self-sustaining cycle of professional growth
  • The Understanding Math Series of programs improves the utilization and effectiveness of existing school/district resources (e.g. textbooks, manipulatives and a school district’s core curriculum and its attendant planning and scheduling time line).
  • Significant return on investment relative to other instructional resources and their costs
  • A sequential and logical system of software implementation that ensures integration into the district’s mathematics program (e.g. correlates with the school district’s benchmark assessments enabling targeted reteaching in areas of needs)
  • A professional development framework that supports the growth of the instructional capacity for mathematics within each teacher
  • NLSI’s commitment to continuous improvement will ensure that all users of The Understanding Math Series of programs have access to the latest innovations in software development and implementation strategies to enrich their mathematics programs.
Sample Sessions

Sample Sessions


Grade Bands: 6 – 8

Go Deep To Address the Common Core; 3 Part Lessons in Algebraic Thinking

This session will share lessons that students have difficulty in understanding and teachers have difficulty in teaching. Participants will receive software and 3 part lessons to "get started", "work on it", "reflect and connect". Participants are welcome to bring laptops to the session to follow the lessons online.

Grade Bands: K – 5

Build It, Write It, Talk it, Now Own It - Go Deep to Address CCSS & RTI

We will demonstrate methods to "hook" students to deeper conceptual understanding by modeling specific lessons involving paper, manipulatives and computer. Participants will receive 3 part lessons to address CCSS as well as all three tiers of RTI and access to software. The lessons will be adapted to a wide variety of learning environments.
Lessons include:

  1. Developing an understanding of fractions
  2. Distinguish between area and linear measure
  3. Analyze patterns and relationships

Grade Bands: 3 – 8

Build, Write, Talk, Own!! Go Deep to Address CCSS & RTI

We will "hook" students and teachers to deeper conceptual understanding by modelling 3 part lessons for all grade levels in many learning environments involving fractions, area, patterning, algebra and more.  Participants will receive access to CCSS standardized tests as well as lessons to specifically address RTI and hence maintain the sanity of the teacher.