Hi to All! Catching up on email this morning and saw this in my inbox due to an old hit to the Subscribe button. I agree with Karen and Ruth; however, my philosophy was a mix of self-directed and horse-to-water coupled with a bit of shove the horse's face into the water till it drinks (when necessary). All three of my kids are grown; our youngest is in grad school. In fact, he is a perfect example of how this worked. He is working on his Master's in Organ Performance at Rice University. His day in high school started with travel to a nearby church with an instrument and then two hours of bench time. Later in the day, there was two hours of piano practice here at home. This boy was very motivated and self-directed when it came to music. Writing? Not as much. The sputtering horse fighting at the trough is a better image. But I did get a call this fall where he thanked me for forcing him to learn to write. One of the classes he took this fall focused on learning to write/speak about music - a good performer need to be able to write and speak publicly about the music he performs. One of the texts was Strunk and White. "Mom, Thank You." He earned all A's this semester - including the writing class. He mentioned that class participation was part of the grade. I asked him if he participated. "Yes, Mom. By the end of the semester, the prof would ask a question with the caveat that someone else should answer." One of the exercises was to rewrite a published article to make it more concise without losing the tone of the piece - hmmm... ever been asked to do that before? When the prof returned his paper, he commented that ds made some revisions that were better than the prof's. This boy would not have gone through Strunk n White, and he would not have practiced writing and then re-writing and then re-writing again if the momma hadn't forced the issue. Now clearly this is NOT what landed him where he is today. THAT was ALL him. The Organ Dept at the Shepherd School isn't interested in writers who dabble at the keyboard. But he can hold his own when it comes to all the other bits because the momma selectively chose the things that were needed: time spent reading, thinking, and writing. Coupled with arithmetic and then math to build the rest of the neural net. And then PLENTY of time to pursue their passions. (Think machete to eliminate the unnecessary and then the self-control to ignore it as I read about all the wonderful things that the rest of you were offering your kids.. psst... not sure this boy has ever read one work of Russian literature - I can check, but I don't think there is one.) None of my kids ever took an AP test; we have a very nice community college with a well-respected honors program within 2 miles of the house. It got them out of the house, taught them how to meet someone else's deadlines, gave them the confidence they needed to face something new, and earned them credits (some, not all) that transferred to their 4-yr institutions. But even those classes didn't interrupt bench-time for this kid. That was always first. A gamble? Yes. Tough to do. But it has paid off. He is happy and thriving. And the others are as well. Peace, Janice Enjoy your Little People Enjoy your Journey

Yes. A wonderful place. He has had a fantastic four years there. Hope things work out for your daughter! Peace, Janie

Hi Sue, It's odd. I'm convinced it's an auditory thing with him. My parents have a piano that is ridiculously out of tune, and he has trouble playing it. In general if you take the black dots/lines away from him, his playing shifts. Everything opens up just a tad. All those years playing violin in an orchestra and listening to orchestras like the one at the Met take over. I think that's part of the reason he loves the organ so much - you have four limbs and TONS of orchestral-like options. What do you want people to hear and when and how? And can you pull it off? You choose the bank of pipes you want - and then you try to deliver the line so that it nests well within the other voices you have chosen. You take a discrete set of pipes and try to create the illusion of a continuous musical line - lots of them - all at the same time. And of course, when you are there and he is pointing out this this light, gentle musical idea that he has sent bouncing off the walls or the room is shaking because of the 16 footer, you can't help but appreciate the craftsmanship of the organ builder, the composer, and the musician. Figuring out that being a part of that was this kid's thing took a while. And I am convinced that when he stops trying to see the music with his eyes, he hears it more clearly with his ears. Because in the end, those dots are just a contrived representation. Just as Plato was stuck trying to use words that he then turned into squiggles to convey what he was trying to think, Widor was stuck using a similar system to convey what he was thinking/hearing to a person in a different place/century. And right now that is the thing that this kid most enjoys thinking about. It really was one of the joys of homeschooling to be able to work with my three little people for years - trying to black-box each of them: Who are they? How do they take in/process/spit-out information and ideas? What kind of information resonates within their box? How does it change after being in there? What do they like? What do they hate? Can we ignore the hates and cultivate the likes or will that hamper them later on? Where is the balance that will help them see what they need to do to become happy, healthy, contributing people in the world where they find themselves. How do they need to fill/clean out/reshape the black-box that is their own headspace in order to be their best self? I remember reading an anecdote offered up by a Columbia University Professor in defense of their Great-Books-required-curriculum. The gist of the argument was that each of us spends our entire lives stuck inside our own heads. That place is one of the few things that is really our own - I am alone in here - and it's all mine! So we owe it to our ourselves to make it the most interesting place it can be. That really stuck with me. This is this kid's jam for now. Who knows what will happen as he paddles along in the pond he has found. He has started reading philosophy. "Mom, you have talked about this stuff my whole life. I didn't really get it till now." He is 21. What fun! Rock on! Peace! Janice in NJ Enjoy your little people Enjoy your journey

Hi All, I'm a bit late to the party with the wrap-up; DS made his decision about a month ago. This fall he is headed to the Rice University's Shepherd School of Music to pursue a Masters in Organ Performance. Full ride, and it looks like he will be slipping into a pretty decent part time position at one of the churches in Houston. He is over the moon, and we are pretty psyched for him. The lad played in chapel last week. The board of the AGO (American Guild of Organists) was on campus for a special event, so the faculty asked him to close the service that morning. It's a long piece - starts @ 19:40, if you just want to get right to the ripping part, try 26:20. https://www.stolaf.edu/multimedia/play/?c=2979 Graduation. Then off to Germany and France to play some organs. AGO convention in July. Then on to Houston. Last kid. Done parenting. Now we just enjoy their company. Dh is doing well. Happy at work @ the Metropolitan Opera - among other things, he just joined the Grammy Board - he is lucky to have such a cool job and I am lucky to enjoy some great opera once in a while. He starting riding a race bike recently for fun - 100+ miles in one ride is not uncommon. Plays in a band. Happy guy and the love of my life. In January, I started a new job with BAE Systems. I work with all electrical and mechanical engineers (I earned by BS in electrical back in '89). I have found my tribe and am having fun every day. So I guess I can say that this whole homeschooling thing worked out. Really well. I started this project in 1999 and nearly 20 years later, I consider this last child's graduation from college to be the final loose end. Done. WooHoo! Rock on, folks - it's ridiculously worth the effort! Peace, Janice Enjoy your little people Enjoy your journey P.S. Follow up a couple of weeks later: the lad played the piece with St. Olaf's orchestra this past Mother's Day. What a wonderful day!

This is FANTASTIC, Gwen! Congratulations! My guy finished his last audition this past weekend. Now, he waits. Fingers crossed for that funded/stipend combo here as well! Boy, do we need it. LOL! Once again - please pass my congratulations along to her! WooHoo!! Peace, Janice Enjoy your little people Enjoy your journey

No. St Olaf operates on a fall-interim-spring calendar. The interim semester last for a month (January). Students use the time to take one time-intensive (typically inter-disciplinary) class, and many students use at least one of their interim sessions to do this abroad. More here: https://stolafadmissions.wordpress.com/2011/01/21/interim-classes-on-campus/ This year, interim ended on January 30th, and the choir left for tour the following day. The spring semester began on Thursday, February 8th, and the choir students returned to campus late in the day on Tuesday, February 13th. They usually miss an entire week of class; this year, it was less. Because of this interim set-up, their spring semester ends a bit later than other colleges. Commencement is on Sunday, May 27th this year. So there is a trade-off with the interim set-up when it comes to summer jobs and internships; however, in general I think it's a pretty good system. Most students take four classes each in the fall and spring and then the one interim class. So 9 classes a year at one credit each for a total of 36 classes/credits. Because of interim, students get a break from running from thing to thing and have the opportunity to focus during January. It might seem like a minor shift, but that zoom-in/pan-out way of thinking about the world is a good exercise. And I suspect this set-up is the reason so many of their students are able to say they studied abroad. One month away from campus is easier to swing financially and in terms of checking all the boxes when it comes to completing your major on time at a liberal arts college. Disclosure: because ds joined the choir his sophomore year and because the choir has an intense ramp-up to tour rehearsal schedule during the interim semester, ds never studied abroad during interim. However, he did have the opportunity to travel with the choir to perform/tour for ten days(?) last June in Japan and South Korea. Fantastic. Here is a link to a video recorded by a church in South Korea. Being a part of a huge worship service on the peninsula last June with everything else that was going on at the time in politics - this - this moment in time - was one of the most significant moments in this kid's life so far. My DS will probably never see any of these people again for the rest of his life, but during this time, within this set of <x,y,z,t> coordinates, they shared something. Music and worship have a significant meaning for this person. So this kind of experience at this point in his life meant so much. And I think helping students find those kinds of events - and they are all wildly different - really, not all students are even looking for a spiritual experience, and the college respects that - helping students experience something significant that helps shape their purpose in life is one of the things the school cares about very deeply. (10 minutes in) Regarding this week of missed classes for Ole Choir Students: Sure, I raised an eyebrow the first time this came up. However, first of all my son is a music major so it wasn't that much of a leap; and second, being a part of this group has had a huge, positive influence on him. Huge! Working with other students of this caliber has done much to make him who he is. And don't misunderstand me - I'm not simply referring to their musical caliber; they are thoughtful, engaging, intellectual young people. What a tribe! Last year my dh and I flew out and spent a couple of days in town visiting folks we know in the area, wandering around on campus, and attending ds's junior recital. This phenomenon of clustering purposeful young people in positive directions is repeated elsewhere throughout the college. The place is filled with intelligent people doing thoughtful things. There is a reason the school made it into Loren Pope's book. I know this sounds like an ad, but there is a reason that Ole's are so passionate about the hill. A special place. Peace, Janice in NJ Enjoy your little people Enjoy your journey

Good Morning, More music from the lad (younger DS). The St Olaf Choir finished their West Coast Tour with their usual February Home-Concert in Boe Chapel. DS (music major - organ performance) is the bass section leader so he was asked to be a part of the recorded intermission interview. He also accompanies a couple of pieces. In a couple of our conversations this fall and winter, we have talked about students handling their schedules. Here are the fruits of the boy doing something that he not only receives no credit for but also isn't directly tied to his major. Tangentially tied, of course - singing, conducting, running sectional rehearsals, accompanying - all good things for an organist - but his major is actually ONLY organ performance - notice the lack of organ anywhere. Ironically, he dropped the extra church music major so he could focus on the bench. Hmmm...it's as if a bio major was working in a chem lab for 10+ hours a week all year on the side - while ALSO STILL focusing on his work in the bio lab. Anyway - this activity takes up a TON of time every week - and it has absolutely NO bearing on his GPA. CRICKETS! But if you appreciate music, I'm sure you will agree that it's time well spent. How can you NOT do it!!??!! No regrets; life is grand! Happy Times To Be Sure! Peace, Janice Enjoy your little people Enjoy your journey https://www.stolaf.edu/multimedia/play/?e=2077

Good Morning, Every Aug and every January, I made/make my college students mock up a sample schedule. Classes - in one color Study time - in another. Two hours outside class for every hour of class. Intelligently placed. Class on a Monday @ 10 AM? It is probably good if you can hit your first study-block within a couple of hours of that. (To review your notes. Write 4-5 sentences that summarize what the lecture was about. Start homework or reading/notes for next lecture) And when planning your study-schedule, pay attention to office hours. Plan your schedule with the intent of using office hours or TA hours.) Side note: Shortly after the lecture is the best place for lecture-summary-time: Did the prof argue a point? Thesis? Support? Counter-arguments? Did the prof prove a theorem? What was it? Did he spend most of the class on that ONE theorem? Then it's probably significant. :-) Was there ANYTHING from the lecture that still doesn't make sense? Make a list. Check office hours. Schedule a visit on your calendar. Back to the schedule: Meals/Laundry/Correspondence time daily (email etc) - Put this stuff on the schedule Clubs/activities? On there! Do you like to stare at the TV? Put it on the schedule (helps them to see how they are spending their blocks) THEN - sit and look at your plan. This is always an eye opener. No matter how many times you do it! IT LOOKS FULL BECAUSE IT IS FULL! This is impossible!?! Gasping! Heavy sighs! All that - 50 hours of WORK is a LOT OF WORK! I put this in bold because it is always a shock. BUT it put them in the right frame of mind regarding the pacing of their days. If they are approaching their week with a come-what-may attitude, they are going to be drowning by mid-terms. If they adjust their pacing to accommodate reality from the beginning, things go much more smoothly. They adapt and they sail on through to finals. They are working to be sure, but they aren't bewildered about how much they should be working. And the schedule is the best inoculation against angst and panic. Really. Everyone has access to a calendar program. This isn't a mental exercise, it's an actual one. Make 'em draw in the blocks. Color code 'em. And then LOOK at it! :001_smile: Then - this final piece. This makes all the difference when done well: Reflect on the past week/Plan for next week - a short block for checking your pacing and your weekly plan (30 mins?). How are you doing? How is the schedule working? Do you need to move things around? Now, think about the week ahead: how should you be using your blocks? Big test coming up? Plan the detail for your study blocks: what exactly should you be doing and when? For EVERY block. That way when you look at your schedule and see Tuesday: 11 AM - it already sets a clear objective for that hour. "Problem set 27" or "Read and Summarize Chapter 18" or "Prepare Study Guide for Chapter 27" A clear goal. (And keep in mind, I always told my kids that a 1-hour block is 50 minutes of work and then 10 minutes of getting a coffee/going to the bathroom/checking your phone. A break. Then back to it - to work - uninterrupted.) The calendar with clear objectives designed on a weekly basis for each hour. My single biggest piece of good advice. Peace, Janice Enjoy your little people Enjoy your journey

Thanks so much for all the kind words. You guys are the BEST! While I used to be around daily, I pop in probably at least once every couple of weeks to see what everyone's kids are up to. I really do miss being in the thick of it all with all of you. You guys really made the difference for me. Hope everyone has a great day! Peace, Janice Enjoy your little people Enjoy your journey

Thank you so much to everyone for the kind words. You all are the best! Every couple of years there are a batch of us with kids moving on to the next thing - four years ago it was trying to make the decision about where he should go as an undergrad. And now he is casting about trying to figure out where he should go to start his graduate work. I was a part of the day-to-day four years ago; it can be hectic - trying to juggle all of the current responsibilities with the added pressure and WORK (and money!) associated with applying to school. And then the waiting... and then the decision-making. Well, we are there again. Right now he is still in the work (and money-spending phase of traveling to audition) phase. Some auditions are done; others are not. So for this to happen at this particular point in time is GOLD. When I worked with my kids and other people's kids on the undergrad app process, I tried to frame this in terms of a positive thing rather than an anxious one. During this time, you have the pleasure of collecting/reflecting and then projecting. The collecting part is taking time to pause and think about the last few years. Usually that means starting with a resume. It's the easiest way to start to MOVE them away from this idea that they are somehow a set of numbers. They are not. They are more than a collection of numbers; their accomplishments can not be summed up with 4-5 numbers. What makes you you? How do you spend your time? What do you value? What are your passions and interests? What do you want other people to know about you? Teach them that life has landing pads where you pause, collect, and reflect. Then you project. What do you WANT to do next. In four or five years, if you engaged in the exact, same process, what might that look like? If you could choose what you would be thinking about? If you could make life happen the way you wanted it to, what would *that* be? All done with the understanding that we don't actually have the power to control everything (or sometimes anything) and of course with the complete humility that we are not actually even a sum of our accomplishments. We are people. Valuable, important human souls. Sometimes things work out and sometimes they don't. Our value stands apart from what we do. THAT is always a thing! But, just for the sake of having some kind of goal - as an exercise - what would you like to be thinking about and collecting/reflecting about in four years.... Anyway - I am happy to report that this kid is working hard and enjoying it. And for this to come at this exact moment? It's just really nice. So sometimes things work out. Who knows what is next? Who knows? But I am sending warm thoughts to all of you with children who are transitioning to the next thing. Because sometimes things are going well. And sometimes they are NOT. Transitions are like that. No matter what, my hope is that you can somehow enjoy the journey. All the Best! Peace, Janice Enjoy your little people Enjoy your journey

This is our younger son, a senior undergrad. Two pieces on this week's radio show. (Bolcom's What a Friend We Have in Jesus and Ferko's Mass for Dedication) They were both at the top of the second hour if you feel like checking them out. http://pipedreams.publicradio.org/listings/2018/1805/ Michael Barone will be interviewing him on the show after he plays this July at the AGO National Convention. Happy Times to be sure! Hope you have a nice night! Peace, Janice in NJ Enjoy your little people Enjoy your journey

Hi! Chiming in with Gwen here. All applications have asked for a transcript; however, I suspect it's more of a sniff test. If you are seeking a Masters in Music Ed, most we have seen ask for a GRE, but it's not requested from performance majors. They do ask for a repertoire list with explanations - what was performed, etc. So if your student hasn't been tracking that, she should. Gwen mentioned a recording round prior to an audition. We have found that depends on the instrument. For example, piano and voice departments have asked for a recording; however, my student plays pipe organ, and the schools he has applied to haven't asked for a recording prior to the live audition. It is important to keep the resume in mind too. In the end, they are looking for strong players for performance programs; however, if your student needs money, it's important to keep an eye on that too. What kinds of jobs are available for grad students? TA for theory classes. Accompanying. Teaching lessons. Etc. In addition to focusing on performance, Ds has tried to gain as much experience as an undergrad in the areas that will make him competitive when it comes to getting the funding he is going to need in grad school - in terms of skill set and leadership experience. In his profession, there is also money to be made in off-campus churches. So for my kid, he has focused on building his resume in three areas: 1. Performance - competitions and recital experience 2. Departmental employment - teaching assistant for theory classes; accompanying for recitals, studio classes (sight reading), and department choirs; singer/section leader in a touring choir (as a section leader, he runs sectional rehearsals) 3. Off campus work: Organ Scholar experience all four years of undergrad His resume has these sections: Music Awards: list of competitions/scholarships won Education: Degree info Solo Recitals: List Experience: Employment and volunteer work in college that make him departmentally employable in grad school Music Activities: The catch all (For example, he has taken voice lessons all four years. He took time this past fall to travel to another state to attend an organ improvisation conference on his own. Etc) I hope that helps. Momma brag here: as a winner in the AGO/Quimby Regional Competition last year, the lad will be playing this summer at the Organ Guild's national convention as one of their "Rising Stars." The program will be offered on Michael Barone's Pipedreams Live Radio broadcast. Should be fun! Peace, Janice Enjoy your little people Enjoy your journey P.S. Editing here. Note: if you look at what Ds has focused on, you will notice the DISTINCT absence of classes/grades. Yes, he needed to get decent grades for the past four years; however, for what he is planning to do, the difference between all A's and having a couple of B's thrown isn't a big difference. For example, A's within his department/major are important, but I suspect no one cares a bit if he earned B's in his gen ed classes. BUT if he had no experience as a theory TA? I'm sure that would be a strike against him. Keep in mind, he received NO academic credit for doing that - for multiple semesters - a VERY time consuming job. His off campus job also consumes a ton of his time as does the touring choir he participates in as a volunteer. (They rehearse for 7.5 hours a week - and that doesn't include the section leader mtgs with the conductor and the prep for the rehearsals he runs. Nor does it include prep time when he is accompanying. But a fantastic experience - YouTube video linked below - it was taken during their international tour (Japan/South Korea) last summer. Ds is accompanying the choir.) Again - no mention of either on his transcript. Competitions on his performance instrument? An enormous time commitment! And relevant for his path - but again - not on the transcript. Said all that to say this: every kid's path is different. So it's important to help them roughly sketch it out and then fine-tune it as you go to help them get their priorities straight. TOUGH to do - because they are in an academic environment that focuses on grades. Which makes the transcript seem like the most important thing. In Ds's case, his classes land almost dead last when it comes to where he is focusing his attention. Odd. Strange. But necessary. In Ds's particular case, the education he receives because of the environment tends to overshadow the education he gets in the classroom. (And I get it - the standard 2 hours outside of class for every hour in class. I have hammered that home since they started taking college classes while in high school. Bam. Bam. Bam over the head with that. However, if you map out this kid's schedule, it is literally impossible. Literally. There is no time left for the priority list. And if he skips that, he can't go where he wants to go. Hence - the priority list dictates the daily/weekly schedule.) Sue: I hear you about the recovering homeschooler part regarding the application process. However, from what I understand, this really is just standard parenting at this point. As in we aren't being helicopter homeschoolers - the "regular" parents are a part of the grad school process to some extent. :-) Kids have to those preliminary conversations with someone about what they want and how they are going to pursue it. No paid person is going to take the time to hash all of this out with them in the preliminary rounds. Once they have a rough draft, then I send them to go talk to the mentors/pros who are paid to help/advise them. Otherwise, the kid ends up being the dog at the new pan - wasting everyone's time because they just don't know how to approach this stuff. WAY less involvement then I had during the undergrad app process - night and day - but still needed to be there on some level. Hope everyone has a great weekend! Rock on! Scroll 9:55 minutes in for accompanying clip. It was toward the end of the tour; you can see how exhausted but happy they all are.

... before you start counting on having the extra cash laying around... Our boys needed extra money for food in college. Until they reached about 22/23 years of age, the boys ate more than 3 squares a day. Younger son (20) is in his senior year of undergrad, and the dining hall is closed by 7:30 PM. He tends to eat his last meal of the day between 10 PM and Midnight. So some of the money saved from our food budget here at home gets shoveled in his direction. Peace, Janice Enjoy your little people Enjoy your journey

I am SO SORRY, SUE. Please send him all our love. Janice

Sue, Praying for your son. Janice

Our youngest is. Apps in. Auditions are next; he's a musician. And yes, it's nice to be an encouraging cheerleader without having to be responsible anymore. :001_smile: Peace, Janice

Hi Quark! This really resonated with me. Our youngest had a strong musical bent. While he was in high school, we allowed him to put that big rock - that very time consuming rock - into his jar FIRST before anything else was added. A luxury? Yes. At the time, I guessed that it was the right thing to do for this kid. We managed to fit the other important things in around the edges, but music always came first. He's in his final year of undergrad, and he is doing well. We did the right thing. I see that your son is at UC Berkeley. He is SO lucky to have you as a parent. I know a number theorist who studied there back in the 80's, and he is a brilliant guy who received a fantastic education. What a world you have helped him find. Nicely done!! Peace, Janice Enjoy your little people Enjoy your journey

Hi Arcadia, I would love to hear what you thought about the book. Thanks, Janice

Hi! I always recommend this one as a starting point. Not because it's easy but because it isn't. Courant's What is Mathematics? https://www.amazon.com/Mathematics-Elementary-Approach-Ideas-Methods/dp/0195105192 It's the kind of book that I will never give up. If forced to flee to a desert island with only a small pile, this one would make the cut for me. Not just because of what it says but how it says it. Peace, Janice Enjoy your little people Enjoy your journey

Arcadia, Yes, complex numbers are another fascinating puddle to play in. I'll never forget the first time I was introduced to the Riemann Sphere. How intensely beautiful! I have much to learn within those waters and am very motivated to play there. Peace, Janice

And yes, actuarial science is one of the peel off locations for kids who discover that they don't really like mathematics even though they are majoring in it. According to industry-standard info: To prepare for an actuarial career, you should take three semesters of calculus, two semesters of probability and statistics, two semesters of economics, one or two semesters of corporate finance, business communications and a well-rounded group of liberal arts courses. The actuarial exams are know for being speed-rounds. It's a well known fact that you have to be fast in order to be successful. And I believe that most people who end up there understand the difference between what they are doing and what a mathematician does. They have taken Real Analysis; they know about Baby Rudin - they have taken a math class that wasn't about numbers. They can tell you that they aren't the same thing. I am suggesting that we could do a better job of helping kids understand the differences BEFORE they start down this road. In my experience, it's not uncommon for kids to land in actuarial science because they either want to make the money or because they found out they were being forced off the road. The former is fine. So is the latter - but the latter can make kids doubt their aptitude and their bent. It chose them instead of vice versa. And that can be tough when you're 21. I don't want to start a war, but it's a thing in undergrad math departments that the kids get divided up and sectioned in their 3rd and 4th year. Some of them are encouraged to become mathematicians. And even among that group, there is a pecking order that happens in grad school. Sometimes for kids who have found their identity in their aptitude, it can be a tough lesson. No, you can't always do everything you try to do. Sometimes you need to do the things you like to do. And the things you are naturally good at. Peace, Janice Enjoy your little people Enjoy your journey

Regarding the higher change-in-major rate: I believe the part of the reason this happens is imbedded in Question #6. What is it like being a math major? What is mathematics like beyond calculus? Mathematicians seek out patterns and use mathematical structures as models. Mathematicians often want to prove that certain statements about mathematical structures are true, and if the models are good approximations of the real world, mathematical reasoning can provide insight about nature and make predictions about the world around us. Mathematics involves a great deal of logic, abstraction, problem-solving, counting, calculation, measurement, and the systematic study of shapes and motion. Many math majors and students of advanced mathematics tend to use words such as "beautiful", "powerful", and "useful" when describing how they feel about the mathematics they learn. Linear Algebra is probably the first course in which students are universally asked to prove that certain statements about mathematical structures are true. Sure, proofs have been there all the time. Students see them. Teachers explain them. And some courses require students to dig into them more than others. However, before LA I think many successful students get away with tuning out that proof business and just waiting for the algorithm. "Just tell me what to do: What formula do I use? How does it work? Where are the practice problems? (Watch how fast and accurate I am!)" Sure, the practice problems involve a level of increasing creativity in order to solve them, so that's what a lot of successful students think mentors mean when they make a statement like this (#8): The study of mathematics involves a great deal of creativity, and it is not uncommon for math students to also be interested in other creative endeavors, such as art or music. Although I think in general that last statement can be misunderstood by high schoolers. I think we are failing kids on that one. Few kids come out of high school thinking that musicians make their living playing scales. Musicians aren't technicians. There's more to it. And few artists are painting by number. Kids have a decent idea of what it takes to succeed as a musician or an artist. I don't think they realize what that means when it comes to mathematics. (AND - many music majors peel off during or after college-level music theory because it's their first non-technician musical activity. Now they get it. They discover that music isn't what they thought it was. I'm sure art programs have something similar.) Back to math undergrads: Because of sequencing, it's important to get to Linear Algebra - usually in year two - in order to have time to get to the good stuff in yrs 3 & 4. (See Note below regarding LA.) So most kids take LA prior to things like Probability and Statistics. Those are tucked around the edges. So if LA was unnerving, many students can feel re-grounded when they land back in those plug-n-chug courses like Probability and Statistics; although by then, most are starting to realize that something is starting to shift. Now when they see those proofs, they know that understanding them makes the difference. You can't tune them out and wait for the algorithm. You're going to get lost. Depending on the school and the course, often an algorithm-only student can pass. But they can't land an A. And they know that something is amiss. Then they hit Abstract Algebra and Real Analysis. That's where the road divides, and students are forced to peel off. Mathematics isn't really so much about being a human computer: find a formula and then work through 15 problems using that formula. We have software for that. The subject is really about proving something is true and then using that certainty to prove that something else must be true - and that can be mind-blowingly beautiful. Stunning. AND once you know it to be true, the irony is that you don't need to work an example. It's a moot point. It can't NOT be true. You don't even want to work an example. Why reduce perfection to a simpler form? You just sit there and wallow in the immensity of the always puddle. Feeling the warm wonderfulness of certainty in an uncertain world. Getting to that moment takes so much time and effort. "Reading" mathematics is a slow and deliberate process. The more advanced the text, the more the reader must bring to the table. No one expects Shakespeare to start with a discussion of vowel phonics and syllabication. The bard assumes you bring a wealth of understanding to his first utterance. Same with mathematics. Each volume is shelved somewhere in the hierarchy, this branching tree that is popping out and expanding at a dizzying pace. People often liken it to music, but the biggest similarity I have found is the way it works in my head. If I'm practicing my scales and my left hand instinctively feels comfortable flying up the keys in G major, then sharing Mozart's ideas certainly becomes easier. It's just quicker. I can do that with little reflection. I understand immediately what he means when he smashes that blur of ink onto the bass clef. Clear intent across time and space. (And if I know what I'm doing, Mozart's blur means something completely different from Chopin's blur. Different intent. Reflect. Process. Play.) In any case, I am free to focus on the bigger idea that Mr. M. is sharing. You can feel your brain shift gears as you move between the mechanics and the art form. That happens when reading mathematics as you reflect on everything that is stored in the various filing cabinets in your brain as you are "reading." Connections. I catch myself handling the ideas that I have come to own. First the recognition. Five symbols on the page, an idea in a language. They mean something. The symbols are a reminder of something I know to be true. Finding that something in my own catalog is the next step. Sometimes it's just an inventory process. Yes. That. Before. After. Where does it land? Why? Got it. Next idea... (Next building block in the proof.) Sometimes the process grinds to a crawl because I can't quite remember the details of why that must be, so I challenge myself. Can I sketch it out and try to pull that mental file to the top of the stack? After all, I shouldn't really be using this block unless I have confidence in its substance. (Sketching it out yourself is the best way to solidify its certainty within the structure of THIS idea. Convince yourself.) If not? Dang it! Best to go look it up. Find it. Read it. Got it. Close the book. Continue with the intent of doubling back the next day to sketch it out again to solidify it. Back to reading. Where was I? Oh yes. This link in the chain that produces an understanding of THIS proof. Again: Previous link, this link. Got it. Next line of the proof... Sometimes I have to stop reading. I'm lost. Time to back up and fill in the gaps. I slide the book back onto the shelf with the hope that I will make it back before this carcass gives up. It's like meeting someone you are eager to talk to, but then you realize that you aren't ready to listen to them. You can hear the words, but you can't find meaning. There's no resonance. It's all just sounds. You need something else first. So rather than fight the process, you shelve the person and their ideas. Time to grow into your own boots. And then you cast about for the steps between what you know and what you just bumped into. Process. Can takes weeks or years. Not for the faint of heart. Can't rush it. Can't move forward till you are ready. Oh well. Time to enjoy the journey cause the destination just faded into the distance. Time for baby steps. Humbling but beautiful. Facing ones own mortality as you realize that you are definitely going to run out of time before you have a chance to enjoy all the flavors available. The difference between big ideas and small ones. And ones that are bigger than big. Sometimes my "reading" slows to a crawl because I make a connection I hadn't made before. You know it when it happens. Now there are two or more ideas in your head that were never part of the same thing. But of course they were all along. You just didn't know it. But now they so obviously fit together. Everything has changed and it's almost as if they have always been together. Except you know they weren't just a moment ago. But now they are. Everything else seems to have sharpened into focus just a tad more. It always was; you just didn't know it. But there it is - as clear as anything you've ever known. When that happens, I usually try to pause to savor the event. It's special. And very satisfying. (I'll admit it - sometimes I've cried. What a rush!) I can feel the spaces inside my own head. It's as if the ideas stored there have a location. A structure. They are connected. And now reconnected in a new way. Such blissful coalescence. Because so much of my experience with that muscle is spent banging around in there trying to remember if we need toilet paper while standing in the supermarket, it is incredibly satisfying to be reminded that this organ is capable of SO much more. Even at my age. In fact, it's only because of age that there are so many fantastic treasures tucked away in this attic. Such bliss. Such peace. And it's all mine! I'm the only one who will ever be in here. Probably the only thing I can ever truly call my own. Such privacy. That happens very infrequently. Most of the time reading math is just work. I do it cause I'm waiting for the next "high." (It's THAT good!) However, to build all that? Takes discipline. Diligence. Hard work - you can feel the stress it puts on the muscle. Glorious! But not the same thrill you get from doing something repetitive like cranking out a page of examples. The hand just moves - with only casual mental effort. And it feels so productive - especially when it's easy for you and other people think it's hard. VERY rewarding. What an ego pump! But that's not REALLY what mathematics is about. Mathematicians are tasked with creating something new. Pure mathematicians prove new things. Applied mathematicians find new ways to use those new certainties. Neither spends her time cranking out examples and then checking to see if she got the right answer. There are NO answers in the back of the book. That thrill of being "right" that kids who are good at math in high school feel - the little endorphin rush that the smart kids get 20+ times every night doing their homework? That's over. A lot of math majors discover that they love arithmetic, not mathematics. They peel off. An example: 1 = 1 1+3 = 4 1+3+5 = 9 1+3 +5+7 = 16 1+3+5+7+9 = 25 Did you notice that 1, 4, 9, 16, and 25 are all perfect squares? Arithmetic asks, "What about the next one? Is that a perfect square too?" Viola! Yes, 36. But maybe the next one will fail... nope still a square. Then +13, +15, +17... Endorphins. Speed. Rush. Faster. Dang, I'm good at calculating things in my head. I feel so smart right now. Next one! The irony is that no matter HOW fast you go, you're never closer to being done. And you are no closer to answering the question. Yup. That. Mathematics asks, "Is this a coincidence? Will this always work? Will the next sum always be a perfect square? How can I be certain? (And I'm not talking about a pile of examples where I give up and decide that it probably always works? I'm talking about how can I be sure!)" Cranking out the next example is easy. Certainty is harder; but it's worth finding. And the journey is glorious! Peace, Janice Enjoy your little people Enjoy your journey Regarding Undergrad Linear Algebra: Keep in mind that a good undergrad LA course makes it clear to students that they are only seeing the tip of the iceberg. These waters are deep. And the more you know, the better. Ask Sheldon Axler. He thinks we are doing students a great disservice by letting them even HAVE the determinant as undergrads.

Hi Gwen! I haven't said hello in a long time. Hope you are all doing well! I often think warmly about the fun we shared launching our youngest kids into this field together. I have only met a few board buddies over the years, and it was SUCH a pleasure to meet you and your daughter. Happy Times to be sure!! I hope you have a pleasant morning!! - Janice