All the material described below can be incorporated into individual tutoring sessions.
To read about titles, dates and locations of previous workshops
(as well as comments from participants) please click on 'References' above.
Customized Workshops [ back to top ]
Workshops can be designed for small groups of 3-6 students or for large groups of a dozen or more, as well as for auditorium-sized presentations in schools. Workshops can been designed for homeschoolers on either an on-going 'semester' basis, or for occasional enhancement and exploration of given topics. In addition to these customized workshops, you will find announcements here from time to time about pre-scheduled workshops open to the public (covering topics described below, under General Interest).
Individual Math Topics [ back to top ]
Real understanding of mathematical concepts leads to confidence and competence. These topic workshops are designed to do more than teach students how to work with numbers and operations: through personal and group explorations, students will discover the underlying meaning and sense - the why - behind mathematical rules and short-cuts. Though some may believe it is simpler and quicker to just learn how to 'do' math, countless children and adults will attest to the fact that, unless they know what they are doing and why, it is difficult to grasp, retain, and retrieve new material. Equally important is the fact that without a deeper understanding of the meaning and inter-relationship of various operations and formulas, students will have great difficulty solving problems that do not look exactly like the given examples. The aim of these workshops is to help students come to feel they finally 'get' it, and can therefore easily recall (or just as easily, re-construct) the appropriate procedures for solving problems. Topics include understanding and working with: Positive & Negative Numbers, Fractions & Mixed Numbers, Exponents & Radicals, Ratios & Percents, Factoring & Prime Numbers, Variables & Polynomials, and many others.
Thematic Mathematical Overviews [ back to top ]
Algebra often marks the beginning of the end for many students. There is a good reason for the confusion that many feel at this stage: math suddenly becomes very abstract. But this confusion can be transformed into a deep understand of both mathematical concepts, and of the mind's amazing ability to create and work with abstractions. This understanding can be achieved by helping students get a broader and more coherent sense of how various mathematical procedures inter-relate, how they were derived, and what 'clues' to meaning and procedures can be found in the names and 'shapes' of formulas. These workshops will incorporate various perspectives and modalities, including the use of hands-on materials, as well as discussion of historical contexts in order to help students get a sense of how mathematical thinking developed over time, and how mathematical thinking develops in the human mind. Topics in these thematic workshops include: Graphing Linear Equations, Solving for Unknowns, Factoring Quadratic Equations, Deciphering Word Problems. Similar explorations can be focused on various aspects of the development, meaning and applications of Geometry.
Thinking, Learning and Study Skills [ back to top ]
Everyone has natural preferences and avoidances in terms of the way they organize information and make sense of the world. For some, their natural tendencies serve them well; while others can feel overwhelmed and 'out of control' in terms of making sense and order of what they perceive and learn. Though it is not always obvious or easy to convey, even the 'chaotic' ways of thinking can be viewed and cultivated as an asset, while the seemingly 'orderly' mind can sometimes be a liability in terms of creative problem-solving. The key is to learn to think about ideas and information in different ways, to find a balance between a wide-angle and close-up view, to complement intuition with analysis, and the concrete with the abstract. In these workshops, students will learn to identify their own thinking preferences (beyond the usual auditory, visual, and kinesthetic labeling). They will learn how brains works in general terms and how they can enhance and supplement their natural cognitive abilities with new tools and skills. Students will explore and discover various problem-solving strategies, inductive and deductive reasoning, critical thinking, personalized ways to organize, store and retrieve information and ideas, and much more. All this is done in a relaxed, non-competitive, though challenging environment among others of varying ages and academic backgrounds.
General Interest [ back to top ]
Many people who are no longer students and have no specific reason for studying math have expressed interest in learning more about mathematical thinking and mathematical concepts. To address some of these requests, I have designed workshops to help people understand why they (or others they know) have had trouble learning math as it is traditionally taught, and how they can reclaim their natural ability to learn math. Other workshops focus on relaxed overviews of some of the topics that adults wish they understood but never did. Still others focus on some of the more interesting and 'mysterious' aspects of mathematics, such as those referred to in The DaVinci Code (Golden Ratio, Fibonacci series, etc.). If you are interested in any of these workshops, or would like to be notified when they are scheduled, please let me know through the contact link above.
Homeschool Workshops [ back to top ]
In general, these workshops will serve to introduce students to new topics, as well as helping students who are already familiar with the topics to gain a deeper understanding of what is really going on, why it works, and how it relates to other mathematical concepts and procedures.
(1) Making real sense of basic (but important and complex) math topics, including operations with positive and negative numbers, fractions, and exponents. Many students are ‘beyond’ this level, but still wish they had a better handle on these essential and recurring topics. This one can be very helpful for all ages and levels.
(2) Solving for X. What’s REALLY going on? How to make meaningful sense of the essence of algebra. And therefore, how to easily figure out what to do when and where and how and why.
(3) Exploring linear equations and graphing. This is a subject that involves all sorts of procedures and formulas but is rarely presented in such a way that the student sees how it all fits together, and that the formulas don’t have to be memorized if they are really understood. This is actually a very cool topic. Very visual, with a fascinating history of its development.
(4) Exploring geometry the Egyptian and Greek way. Using ropes, sand, cubes, etc., as well as a compass and a straightedge, students will discover and derive (rather than have to memorize) the foundational elements, formulas, meaning, and beauty of geometry.
(5) Word problems: How to make sense of them, why they’re hard for almost everyone, and how they can serve to build very important general thinking skills.
(6) Ordered Chaos: A real catch-all workshop where kids of different ages and levels come together with confusions and questions about the math they have been learning. Though it sounds like potential madness, it would provide a perfect setting for valuable skills that homeschoolers often miss (as do public schoolers!), including: team work; cooperative and supportive teaching and learning; an opportunity to teach what you know to others (which helps you understand it better); a chance to share your unique ideas about alternate ways to tackle challenges; a chance to struggle with others in a safe and comfortable atmosphere. Lots of exploring. Lots of surprises. Lots of challenges. Lots of self-confidence.
(7) Developing Cognitive Skills: This workshop will help students explore, discover, and invent strategies and skills that suit their individual needs and enhance their natural abilities to focus, comprehend, organize ideas, problem-solve, etc. As part of the workshop, students will learn how brains work in general, and how their own brain 'prefers' to function.
Cost and Scheduling [ back to top ]
Workshops can be customized to suit the needs of small and large groups. Cost will depend on number of participants, duration of workshop, and materials used.
Contact Noa [ back to top ]
Feel free to contact me for more information at 615-269-7526 or by clicking on the e-mail link at the top right corner of this page.