April 2009


To Fellow Homeschoolers (and others devoted to teaching children in the most inspiring, nurturing, powerful, and efficient ways):



         My 10 year-old daughter Sophia and I found a unique and splendid math program last fall.  We want to share this treasure with other families who will benefit as profoundly as we are.  So many people struggle with math, and don't really like it -- this program totally changes that. 


         CIMM (Cognitive Instruction in Math Modeling) is a whole new approach to learning math, which is being developed by a brilliant mathematician, Dr. Rob MacDuff, and his team of physicists and mathematicians with support of the ASU Physics Department’s Modeling Instruction Program. 


CIMM is based on neurological principles.  It presents a joyful and powerful alternative to the fragmented, disembodied, rules-based mathematics curriculums of our modern age.   


I didn't know how terribly limited the math options were until we started CIMM. Sophia and I were pretty happy with our math studies.  We had gotten a splendid early start through The Institutes for the Achievement of Human Potential, whose training and resources helped us immensely when Sophia was very young.  (IAHP website: http://www.iahp.org/) But we noticed that it became harder to maintain our momentum of inspiration as we progressed further into the available math appropriate to her advancing “grade” levels.  I had done quite a bit of research and put together the best program I could come up with, using a combination of top quality materials from several standard texts, plus Math-U-See, Oak Meadow, and our own creative explorations.


But this CIMM is a whole other world.  It is utterly fascinating and engaging, and its elegant sequence of lessons teaches an astonishingly deep level of mastery so quickly and joyfully.  I am consistently blown away by it, and so grateful to have access to it. 


         Sophia has gone from feeling like "math is okay, but there are so many other things I'd rather be doing, and I'm not that great at it anyway..." to "WOW!  I LOVE math!  Can we do it for another hour now?!"  


She is gracefully grokking these mathematical concepts and skills that were more vague, elusive and boring for her before.  And she is loving every moment of it!


And I'm learning right along with her -- finding my own sense of mathematical competence, clarity and enjoyment growing and flowing in new ways, too.  This CIMM frees up places in my brain and my thought processes which have been seized up, stunted, shut down -- thanks at least in part to the math education I received in the "top" schools I attended before college, and at my Ivy League university (Cornell)...


Teachers trained by Dr. MacDuff have been teaching CIMM in several schools.  They are seeing exciting results, both with students who've been struggling with math, and students who are strong in it, and the CIMM prepares so exquisitely for advanced math and science.  There is growing demand for CIMM – which is outstanding news for all the students and teachers out there struggling through the gamut of standard (ie., limited and corrosive) approaches to learning math.  


I first learned about Dr. MacDuff’s program through my interest in David Hestenes’ work.  Dr. Hestenes is one of the great physicists, and teachers, of our time.  He runs the Modeling Instruction Program in the Physics Dept. at ASU, along with his intrepid colleague, Jane Jackson. 


Dr. Jackson introduced us to Dr. Chris Horton, who is working with Dr. MacDuff on writing the CIMM curriculum, and Sophia and I are blessed to be learning CIMM with his help.  Chris is tutoring us in the comfort of our home, via iChat.  


Chris Horton is wonderful!  He is a Ph.D. physicist; a skilled and experienced math and science teacher at all levels, from children around Sophia's age and younger, to adults learning advanced calculus and physics; and he has a beautiful command of CIMM.  Plus, Chris is wonderful with children, and grown-ups, and he is just a warm, sincere and lovely human being.  I most highly recommend Chris, and this process, to anybody looking to improve their learning curve in anything math-, science- or logic-related.


Chris’ rates are very reasonable, astoundingly reasonable for what you get.  He wrote the enclosed announcement, to let people know about his tutoring services.  I asked him if I could show it to some great people who might be interested, and he agreed.  I will attach it below -- and it has more good information about CIMM, too.  


Also, Dr. Rob MacDuff teaches programs for educators at all levels, providing them tools and understanding to teach CIMM in their schools.  I hear those programs are superb, too.  Dr. MacDuff is a splendid, wise and exceedingly generous person and teacher, so if any of you want to bring CIMM into your local school systems, those trainings would be a golden opportunity for you, too.  Here is the website: http://modeling.asu.edu/CIMM.html .


CIMM is a joy.  The kids who are fortunate enough to experience it will love learning math.  Plus, CIMM’s coherence, clarity, and power catalyze ability and confidence in every other line of study, too.  And CIMM gives children inspiration and potent tools to contemplate the world around them, to problem solve, to understand whatever they put their minds to, to design the practical steps necessary to bring their finest dreams into reality, to trust themselves – little things like that…



Julianna  Parker



See Chris’ announcement below:


        I can help your children love learning math and excel at it - joyfully and immediately! 

        I offer a lively, innovative curriculum - that will prepare your child for advanced mathematics in a light-hearted and thorough way - with a tutoring style based on a deep respect for children and how they learn best.

        My promise:  Your child will develop a lifelong love and appreciation for mathematics.  In one year, your child will acquire the skills and understanding for complete success in algebra and geometry.


This process is available by Internet Web-chat - or in your home in central Massachusetts - for children (age 7 or up), individually or in small groups.  It is also a pleasure to teach to parents and their kids together, or to adults.  (You, too, can love and excel at math -- it's never too late!)

The deal:  My charge is $25 for one student per hour, $5 for each additional student. Call me for rates for larger groups. I recommend at least two one-hour or 90-minute sessions per week.  No prepayment required, but you need to commit yourself to keeping to a schedule.  If after the first five lessons you and your child aren't completely satisfied I will cheerfully refund your money.  

Special challenges:  Teachers report that this curriculum works amazingly well for for English language learners and for students with ADD and developmental differences such as AS or HFA.  

System Requirements for online classes and tutoring:  iChat or Skype with a webcam, a fast Internet connection (400 kbps bandwidth might be enough) a recent, fast processor and 1 GB memory.  Maximum: 3 Web-cams, 3 students per web-cam.  Contact me to schedule a system test or to explore other possible technologies. 

About me:  I am a PhD physicist, and have taught mathematics and physics - remedial through advanced - in high schools, colleges and universities. I am certified for Math 9-12 and Physics 9-12 in Massachusetts. I am helping to develop this curriculum along with Dr. Rob MacDuff, and have had excellent experiences teaching it to children of ages 7 to 12 and adults, including elementary school teachers. 

Christopher Horton, Worcester MA

508-853-0918 (landline),  MathDoctor@me.com  


References, testimonials, resume and credentials:  Available on request.

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More About the Curriculum:

This carefully designed curriculum, Cognitive Instruction in Mathematical Modeling (CIMM), offers a unique and powerful experience of working with quantity, and takes the mystery out of numbers and numerical operations.  

The essence of this curriculum is that it teaches a mathematics of quantity and relationships.  This mathematics is built on the observable properties of quantities, like a science or like geometry, rather than on a set of mathematical assertions or axioms.  Students are given mathematical tools to think with and tools to express mathematical ideas.  By applying these tools in carefully prepared experiences, students succeed in constructing their own understanding and in clearly communicating it - and they find both the process and the knowledge gained greatly rewarding and enjoyable.  By working with quantities of dots in parallel with systems of symbols and numbers and with verbal descriptions, multiple parts of the students’ brains are engaged and coordinated, resulting in deep conceptual understanding.

Multiplication and division, negative numbers, ratios and fractions, very large numbers and very small numbers, symbols and equations - all make perfect sense and become easy to use.  Students gain a deep sense of understanding, confidence and delight in mathematical ideas.


April 2009