Nothing tells this story better than the emails I have received over the past now almost ten years, beginning with this first one, which mentions Karen Pryor, a goddess of behavior change, a world-famous author, and a friend.

8/12/12
*Richard,*
*My friend, Karen Pryor, suggested that I contact you. *
*My fifteen-year old son, Joshua, will be entering 9th grade at Concord-Carlisle High School. He's had a tough couple of years in school. We've done much testing and have been much puzzled! He tests in the exceedingly bright range, and yet struggles with math. We brought in a math tutor last year, but did not see improvement. Joshua works with a terrific cognitive behavioral therapist, who has finally diagnosed a form of math disability. We have decided to homeschool him in math this year. The high school is on board with this plan.*
*We need to find a homeschooling program appropriate for Joshua. We also need to find a math tutor to work with Joshua three days a week. His father, Robert, is an MIT graduate, and capable of helping with the daily work of advanced math.*
*Your school is too far for us to travel to on a weekly basis, but perhaps you can recommend a tutor for Joshua to work with? We are still in the process of figuring out how to proceed. Perhaps an evaluation session with you would be a good idea? Is there definitive testing that would help us to decide what to do?*
*Thank you for your time.*
*--Lisa G__*
*PS Karen, Joshua and Robert go to the Boston Symphony together. She knows Joshua well, so I was encouraged when she said that she knew someone who could help!*

Joshua was as happy as you could imagine coming on a one-and-a-half-hour drive after school. We had no one near them, and at the time Robert and Lisa did not think he would be willing to work for an hour remotely. So the drive was a built in part of the experience for Joshua. He came once a week, arriving on Thursdays at 4:00 to work with Ashley, our wonderful math tutor. And for the first several months he was very passive, and he only *worked* at the Factory. His homework and study were not happening at home, or at least not with the needed focus and intensity. The scary part of the plan, given his math phobia, was that he would take a mid-semester and a final exam in the principalâ€™s office when he was ready to do so.

I was worried about his level of effort and his passivity, however that changed when we asked Robert to work at home on basic math skills. We time and chart our student performances, but we had been focused on getting through geometry and did not want to give up time on that, so we asked Robert and Joshua to work on these skills and chart them at home. They produced a chart that was the most extreme and exciting I have ever seen. In two weeks, Joshua went from 10 per minute on multiplication facts to 130 per minute. Before that I donâ€™t think Joshua had ever experienced that he could change and change dramatically on something that had been so difficult for him. I have never seen anyone else do better than 100 per minute on this task. It was immediately clear that Joshua had special skills that were about to come forward and transform his work.

With that amazing increase in skill, he began to work with interest and passion. We added a summer tutor, Sarah, who was young and an engineer in the making. She and Ashley worked in tandem to begin using this newfound joy in math to prepare for the mid-year exam. They were both impressed by Joshua's new energy and rapid learning.

But I remained very worried about his progress, because, while he was doing wonderfully with us, he was going to have to take the midyear and the final exam in the principalâ€™s office at the high school; He had refused to walk into a math classroom previously. Ashley and Sarah were not at all worried and the day came in July. He got a 93! He worked all summer and finished the remainder of his geometry course. He stopped driving down and worked with Skype, which we were already using with dyslexic readers at the time. He went on a major boy scout camping expedition with his dad and missed a week or two while they flew all over the place. He went into Algebra 2 at the HS, and he no longer needed us, being very confident about math. However, he didnâ€™t take the geometry final, and September and October went by as I continued to stress! WHEN would he finally take the test? What if he didnâ€™t do well since we were not around to provide any reviews or preparation?

He took the test in the middle of November! He got an A! From there on Joshua became THE outstanding math student at one of the best high schools in Massachusetts.

*Hi Richard and Ashley,*
*Here's what the CCHS math dept. head has to say about Joshua's geometry final:*
*Joshua earned 93% ---- when I saw him last week he told me that he's doing well in Alg 2 ---- I'm glad your plan worked out so well for him!*

Joshua did not stop there!

2/10/14
*Hi Richard,*
*More good news from *Joshua's* high school. He finally has a math dept. that sees his potential. We had a meeting with his Algebra II teacher last week, and she said:*
*"Joshua is so fast. He will see 3 different ways to solve something, and none of the other students will do it those ways. *Joshua* will explain what he's doing, and none of the students understand what he says. But *I* understand it, and he is wonderful."*
*She could not believe it when we said he was almost flunked in 7th grade math.*
*Thanks again for all your help.*

And the final grand flourish of High School math.

*6/4/16*
Joshua* has an A+ in Intro to Calculus. He got a 105 out of 100 on his last quiz! He was the only student who figured out that the definite integral they were supposed to solve actually had an undefined result (divide by zero).*
*He's starting this fall at Colorado School of Mines in Golden, Colorado. Mines is a fantastic engineering school.*
*Thanks for all your help!*
*Robert G__*

6/4/17
*Hi Richard,*
*Joshua had a great first year at Mines. He did well in calculus (way beyond what I remember) and is looking forward to more calc next year, as well as more physics. He seems very nonchalant about his whizzy math abilities. I know he helped out some of his fellow students.*
*Thank you all again for helping him get over his bad experiences in grade school. Count him as one of your big successes!*

2/22/22

*Hi Richard,*
*What a timely email! We are visiting Joshua this weekend. He is finishing his MS degree in Mechanical Engineering this May (Colorado School of Mines).*
*He's taking classes like this:*
*MEGN502. ADVANCED ENGINEERING ANALYSIS. 3.0 Semester Hrs.*
*(I) Introduce advanced mathematical and numerical methods used to solve engineering problems. Analytic methods include series solutions, special functions, Sturm-Liouville theory, separation of variables, and integral transforms. Numerical methods for initial and boundary value problems include boundary, domain, and mixed methods, finite difference approaches for elliptic, parabolic, and hyperbolic equations, Crank-Nicolson methods, and strategies for nonlinear problems. The approaches are applied to solve typical engineering problems. Prerequisite: This is an introductory graduate class. The student must have a solid understanding of linear algebra, calculus, ordinary differential equations, and Fourier theory. 3 hours lecture.*
*You helped him get on track for some serious math!*
*He has a professor who is trying to convince him to get his PhD working with her. That's quite an endorsement for his abilities.*
*He's a TA for Senior Design Lab, and also working in the Explosives Research Lab. He's helped with research work and should soon have his name on one or two published papers.*
*We will tell Joshua you were asking about him.*

Richard McManus

Hingham, 3/9/22

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