I’m already adding to the Chromebook School: Math post–this time, with a great discovery via The Homeschool Scientist, who recommends their app–which purports to teach algebra to kids from age 5 on. In addition to “Algebra 5+”, they have a number of other apps for building number sense, or learning geometry and going to higher-level algebra. (Later, after having my daughter play the first few levels: great mechanics, horrid aesthetics! Use at your own preference.)
This is a Chromebook School post, about a few math-related web apps that we are using, hope to try, or just find intriguing.
- MathSeeds, (AUD 60/yr, ages 3+), from the same company as Reading Eggs, has proven a great introduction to math. Our almost-five-year-old is well into the “first-grade” portion of the program, which has a nice progression and a variety of games and exercises. I recommend it. Downsides include the fact that it’s quite scripted rather than adaptive, and their early introduction of “number words” assumes some early-reading ability, an assumption that seems unnecessary and un-helpful.
- XtraMath.org (free) is a completely-free site to help kids review and build fluency with math facts. It’s not flashy, but seems effective. It adapts to a child’s particular needs.
- Reflex math (USD 35/yr, grades 3+) also works to build math-fact fluency, along with some helpful teaching methods. It involves a number of fun games, with extra “hazards” thrown in besides the solving of math problems. Our 4-year-old daughter, who has a high aversion to failure, found some of these challenges too challenging–and it also requires keyboard input, which was a barrier for her. For the intended grade-2+ market, I’m guessing it’s likely to be a hit. (The site uses Flash, though I believe they intend to transition away in the next year or so.)
- Redbird Math (USD 80/quarter, K-12) at GiftedAndTalented.com looks amazing, though we haven’t yet tried it out. It’s an adaptive curriculum, based on Stanford University’s research into methods of educating gifted students–which they’ve found actually benefit students across the spectrum. It weaves in a lot of STEM video content, connections with real-life, digital manipulatives, digital projects, coding-related content…wow. As noted, we haven’t tried it yet…but I suspect it will be hard to resist the pull.
- DragonBox Math (USD 5-8 for several apps, Android/iOS) looks like a lot of fun. I discovered it through The Homeschool Scientist, who recommends their app–which purports to teach algebra to kids from age 5 on! In addition to “Algebra 5+”, they have a number of other apps for building number sense, or learning geometry and going to higher-level algebra. (Later, after having my daughter play the first few levels: great mechanics, horrid aesthetics! Use at your own preference.)
For future reference
I’ve come across a few sites that I’m guessing will be useful a few years from now. No experience with them yet, except for the wonderful Khan Academy.
- ExploreLearning Gizmos covers grade 3 to college, with online math and physics simulations.
- Uzinggo.com looks interesting for math and science from grades 5-12.
- Maths-Whizz (K-8? GBP 99/yr) looks interesting, an adaptive curriculum.
- Khan Academy (free), of course, has a collection of good video explanations–along with practice problems, a content map, and a brilliant spaced-repetition system to review at just the right time.
- Beast Academy takes an interesting comics-based approach to math in their print version, and promises an online version in 2018.
I can’t resist tossing in a few offline options:
- We plan to use Math Mammoth. (We’re now in the very earliest stages.) Inexpensive, conceptual, mastery-oriented but with good review. Purchasable as PDF.
- Judging RightStart Math by a video I just saw from someone associated with it, I’m intrigued!
- We’re dabbling in Miquon Math, which uses Cuisenaire rods and a fairly discovery-oriented approach. (Available in PDF from CurrClick.)
- We’re planning to try out MathTacular–haven’t done so yet, but it looks like an intriguing supplement.
- …and finally, I love the idea of “literature-based math” that drives Life of Fred. Some people love it. I’m not completely sure, based on samples, about whether I–or, more importantly, my daughters–will love it as well.
Do you have other great resources to share? Add them in comments.
I studied at home through 12th grade, and we’re planning to teach our daughters at home as well. I loved the experience (including the memory of getting up at 6 AM to do math with my dad), and love the idea of helping our daughters wake up to the world of knowledge. That will involve a lot of hands-on teaching, and a lot of learning woven into real life. I’m also realizing that it’s likely, unexpectedly, to include a fair amount of “screen time”. This is partly because we live where it’s hard to ship paper curriculum, partly because of schedules…but partly because the selection of digital resources is so rich! We’re getting the kids Chromebooks (for educational apps, reading, music, and audiobooks) soon. Some of the Web apps they’ve been using on Mom’s and Dad’s computers will migrate over, and a world of new ones will become options as well. I’ll share a few of the online resources I’ve found in various posts, and try to index those posts here.
Bear in mind that I do see “Chromebook school” as a fairly impoverished approach, if that’s all one’s doing. I don’t, however, have any intention of this being all we do with the kids. I expect the future to hold lots of lovely books, free and creative play, table games for the sake of play or with an academic goal, household science experiments, Lego robotics, art, music, emotional/social intelligence, fun exposure to languages and cultures…and, yes, math worksheets, writing assignments, and all the other “3R-y” parts of school. Activities involving wandering through the woods or tossing a ball also seem like lovely ideas, but living in a flat in a megacity may limit some of these possibilities. (Though I’m sure we could come up with some great nature studies re. particulate matter concentrations in the air, or of the behavior of crows!) As part of a holistic approach to school, though, I’m ecstatic to have online curricula and educational resources available!
Note that there’s a bit of irony in this series: as I’ve researched the various apps available, it’s become apparent that while many apps are available both in Android and iOS flavors, a number of interesting apps are iOS-only. And so…while I still prefer the ethos of Android, a Chromebook or Android tablet may actually not be the best device if you’re looking for kids’ educational apps.
I started whetting my taste for computer programming when my family didn’t have a computer. We actually had had one earlier, a Radio Shack TRS-80 that my dad had purchased, and upgraded to 768KB of RAM. I’d enjoyed playing Asteroids-style and other ASCII-graphics games on its green screen. Eventually, though, the TRS-80’s floppy drives gave out, and we were without a family computer for several years.
During this time, we loved going to the local public library. We’d go with half-bushel laundry baskets, and come home with them full of books. I loved browsing the shelves, finding mysteries, biographies, fantasies…and a few lovely books, designed for kids and filled with arcade-style graphics and BASIC code for simple computer games. When we finally got another family computer, a Packard Bell 486-DX2 66Mhz with 8MB of RAM and a 540-MB hard drive, running Windows 3.11, I was ready to go! With Microsoft’s QBasic language bundled with DOS, I had fun writing my own small programs–even getting as far as a visualizer for the Mandelbrot set (courtesy of A.K. Dewdney’s The Armchair Universe, also from the public library). And when I realized that Microsoft had even included the QBASIC source code for several games, Gorillas.bas and Nibbles.bas, I was thrilled!
The CodinGame site seems to do a great job of re-capturing some of that early sense of wonder at what one can do with just a bit of code. It uses dramatic graphics (such as the Space Invaders-like shot above), but has you write the code to solve each puzzle. It’s simple enough for coders just starting out, but also has more challenging puzzles–and support for many languages. If your niece wants to learn to program, if you want a nice set of C++ (or standard-library) kata , or if you’re an expert developer and want to learn Ruby, Swift, Go, or Rust…this may well be the game you’re looking for.
If the stories, graphics, and online environment of CodinGame aren’t doing it for you, also check out Project Euler, for a set of basic-to-challenging problems to be solved in the language of your choice.
I’ve been reading–listening to, actually–Marcus Aurelius Antoninus’s Meditations recently. He was a Roman emperor, and a Stoic philosopher. My worldview differs substantially from his, most significantly in my understanding of divinity and humanity. As I read his writings, however, I find much overlap in our philosophies, and much to learn from.
On those who oppose us:
In the gymnastic exercises suppose that a man has torn thee with his nails, and by dashing against thy head has inflicted a wound. Well, we neither show any signs of vexation, nor are we offended, nor do we suspect him afterwards as a treacherous fellow; and yet we are on our guard against him, not however as an enemy, nor yet with suspicion, but we quietly get out of his way. Something like this let thy behaviour be in all the other parts of life; let us overlook many things in those who are like antagonists in the gymnasium. For it is in our power, as I said, to get out of the way, and to have no suspicion nor hatred.
But being on guard against everyone isn’t a great option either. Simon and Garfunkel described this poetically in their song “I Am A Rock”; C. S. Lewis, in The Four Loves, says this:
There is no safe investment. To love at all is to be vulnerable. Love anything, and your heart will certainly be wrung and possibly be broken. If you want to make sure of keeping it intact, you must give your heart to no one, not even to an animal. Wrap it carefully round with hobbies and little luxuries; avoid all entanglements; lock it up safe in the casket or coffin of your selfishness.
But in that casket — safe, dark, motionless, airless — it will change. It will not be broken; it will become unbreakable, impenetrable, irredeemable. The alternative to tragedy, or at least to the risk of tragedy, is damnation. The only place outside Heaven where you can be perfectly safe from all the dangers and perturbations of love is Hell.
I won’t try to integrate these thoughts right now…but both are gems of wisdom.
Farnam Street reviewed Nick Hornby’s Ten Years in the Tub: A Decade Soaking in Great Books. I haven’t read it yet, but definitely will–just read this paragraph cited in FS’s review!
Francis Wheen’s book and Paul Collins’ Not Even Wrong were advance reading copies that arrived through the post. I’m never going to complain about receiving free early copies of books, because quite clearly there’s nothing to complain about, but it does introduce a rogue element into one’s otherwise carefully plotted reading schedule. I had no idea I wanted to read Wheen’s book until it arrived, and it was because of Wheen that I read Lewis, and then Not Even Wrong turned up and I wanted to read that too, and Buchan’s Greenmantle got put to one side, I suspect forever. Being a reader is sort of like being president, except reading involves fewer state dinners, usually. You have the agenda you want to get through, but you get distracted by life events, e.g., books arriving in the mail/World War III, and you are temporarily deflected from your chosen path.
I already know I like the guy. Check out Farnam Street for the full review.
If you want to maximize your learning-per-reading-time, you should probably forget about my blog and read Farnam Street. I like learning about cognition, learning, and productivity; Shane Parrish at Farnam Street seems to live a life immersed in such learning, and does a great job of boiling it down for brief presentation. If you must stick around here, though, my WordPress stats will be thrilled–believe me, every page view shows up as a substantial percentage!
I just finished reading Bounce: Mozart, Federer, Picasso, Beckham, and the Science of Success, by Matthew Syed. Syed is a journalist and a several-time Olympic competitor in table tennis. In this book, he makes a great case that practice is what builds skill, with “talent” or “aptitude” often being mostly fiction. I recommend the book–the content is valuable, and it’s an enjoyable read.
Syed offers a number of interesting case studies. A few among them:
- His own experience–in retrospect, he wasn’t exceptionally talented, but had the right opportunities for a lot of coaching and practice.
- “Clusters” of elite runners–determined not by genetics, but by environment and experience.
- An educational psychologist who set out to prove that training, not talent, determines chess skill. Before he was even married, he proposed to train his children to elite levels of skill. Two of his daughters held the top two rankings of female chess players in the world.
Syed also offers some other great nuggets. Among them, he looks into why high-level athletes “choke”, apparently losing all ability to play, and why athletic skill isn’t necessarily transferable across sports. In a great anecdote, he describes deploying his table-tennis reaction times against a tennis player’s famous high-speed serve. The results…well…didn’t convince him to switch sports.
Bounce echoes themes of psychologist Carol Dweck’s research, much of which is presented in her book Mindset. I highly recommend Dweck’s book as well (despite a fair amount of “fluff”), both for personal growth and parenting. I expect there’s also a fair amount of overlap with Geoff Colvin’s The Talent Code, but haven’t yet read Colvin’s book.
On quizzes and big exams
When I was in college, most of my grades were based on some combination of assignments, quizzes, and–heavily weighted–the mid-term and final exams. If I bombed a quiz, I wasn’t happy about it, but it wasn’t a major disaster. If I’d completely failed a final exam, though, it would have been a Big Deal.
In the years after college, I sat for the three levels of the CFA exams. Multiple months of focused study, a cost of $600 for a given exam, a six-hour proctored exam given only once* a year, driving up to Kansas City the night before to stay in a hotel close to the test center…for me, passing these exams qualified as a Big Deal.
The thing is, I didn’t actually sit for three CFA exams–I took somewhere between six and a dozen exams, across the three levels. Fortunately for my sanity, my work, and my marriage, most of these exams were “practice” exams–exams that I “proctored” for myself, that I graded myself, and that I used to figure out what areas I still needed to work on for a given level. By the time I sat for the “real” exam, I at least had a good idea of the “shape” of my knowledge, and a very general idea of how I might fare on the officially administered exam.
When I finally sat for a given level of the exam, failing it would not have been fun–but, if I’d failed and re-enrolled for the same level the next year, the first try would have given me both resources and lessons to help in the second round.
You see, life is practice. Very rarely is a “test” really a final exam. Losing a job, failing in business, damaging a relationship, missing a big opportunity–each is unpleasant, but each is recoverable
Galton boards and conscious navigators
I find it easy to think of life as though it’s a Galton board. You’ve probably seen one, though, like me, you might not have known what it was called. It’s a triangle of steel pins, where a marble dropped into the top of the triangle falls in a random sequence of “lefts” and “rights” on its way to the bottom of the board. And once a ball falls on the left side of a pin, a part of the right side of the board is forever closed off…and another leftward fall closes off more of the right forever. And there’s some truth in this. If you let yourself get addicted to drugs or alcohol, it’s really, really hard to move out of that section of the board.
As like a Galton board as life may be, though, we aren’t falling marbles under gravity’s control. We can–through our own volition, and sometimes through others’ interventions, take unexpected paths through the maze. We can backtrack, take unexpected paths, sometimes even jump across gaps in the maze. We might be falling through Galton’s maze, and gravity and randomness can predict a lot about where we’ll end up–but they don’t necessarily get the final word. If I start with a couple of rightward choices, I could still end up at the far left of the board. Choices matter, but they’re usually much closer to quizzes than to final exams.
Of course, your life will ultimately end, and it will be somewhere between “wonderfully lived” and “wasted”. But until the grades are turned in, it’s all practice.
Please let me know your thoughts. If you want to affirm or elaborate on what I’ve written, to express disagreement with it, or to help sharpen my writing or thinking, I’d love to hear from you.
* Actually, Level 1 of the CFA exam is given twice a year, in June and December; the subsequent levels are only in June.
This morning at the breakfast table, my eldest daughter “needed” help with her food. We helped her get started, but for finishing the challenging task of stirring her oatmeal, her mom encouraged her: “We do hard things.”
Without premeditation, we’ve started using this phrase recently in our family. It may not be as hardcore as Sara Blakely’s “What did you fail at today?” question, but it’s a lovely phrase. It encourages a growth mindset: “hard” is good, not bad. It makes it a part of our daughters’ identity, much like saying “I don’t” instead of “I can’t” re-wires the brain to help with goals. And it builds a shared identity–we, the Iwashige family, do hard things!