I created Matheno for one simple reason: to help students do well in their college-level science and math courses.
As a former Physics faculty member at UC Berkeley, I’ve worked with many beginning students from diverse backgrounds. Most work hard to do well, and many succeed greatly. But others, despite the same amounts of time and effort, do significantly less well. There are of course many reasons for this difference, but I’ve noticed one enormous distinction worth highlighting:
- Less successful students put their focus on getting through each week’s homework, and then review somehow for exams. While they typically become comfortable with routine problems, they can barely complete each assignment’s most challenging problems, and certainly never go beyond that level. Then since test problems tend to be of that challenging variety (or even a bit beyond), these students often find themselves unprepared for exams. And so they struggle.
- By contrast, other students go beyond routine homework problems, and also become proficient—through continued practice—at more challenging problems. By practicing harder problems, these students find exam problems more familiar and so are able to complete them more comfortably. And so they do well.
That’s it. That’s the big difference.
Of course it’s challenging to go from not knowing anything about a new topic to being able to solve college-exam level problems in a subject like Calculus. . . but you wouldn’t be here if you weren’t facing that very task. And we believe that with the right resources and support, you can.
that has to get rewired.
A key point to all this is that you have to become good at solving exam-level problems. Watching your professor won’t do it; watching a video lecturer won’t do it; reading someone else’s solutions won’t do it. Instead you have to get stuck, make your own mistakes, and think things through, pencil in your hand—these are all crucial steps to learn anything that’s challenging. It’s your brain, after all, that has to get rewired to permanently encode your new knowledge.
Simultaneously, you don’t want to spend hours struggling to solve problems that are beyond your current skill-level; otherwise you’re just getting good at, well, struggling. And spending a lot of time searching for online solutions ultimately isn’t very helpful either: then you’re practicing your searching skills, which you won’t be able to use during an exam.
So we’ve set out to provide you with good problems to use for practice, that come with complete solutions—including lots of explanation in English. You work on the problem using pencil and paper (just as you will on the exam), get as far as you can, and then click to reveal the solution. You can quickly check your answer, and see every detail of the solution. If you got the problem right and think you could easily solve it on an exam, mark it “Green: I’m fully confident” and move on. If you got it wrong because of some minor errors, or were just a little stuck, mark it “Yellow: I’m mostly confident, with some details to review.” And if you made a major error or didn’t know how to begin because it’s still too new, mark it “Red: I’m not yet confident, and so definitely need to review.” When you revisit the topic later, you’ll easily be able to see where you should focus your time: on those problems at your current “learning edge.”
We all have to make mistakes—sometimes lots of them—when we’re learning something new and challenging. So make them here, without penalty, and celebrate that you’ve made them now rather than on the exam itself. And over time, by focusing your efforts on the pieces you couldn’t do earlier, you’ll find that your problem-solving abilities increase so that those harder problems are now routine for you.
Of course we also have some easier problems on each new topic as well, to help you come up to speed before we start applying the new ideas to harder problems. Use those as a starting point; then build your problem-solving abilities up to where they need to be so you enter your exams feeling confident and ready. Finally, just execute what you’ve already been practicing.
We’re committed to helping you learn well in your science and math courses. Indeed, the word matheno means “learn” in Greek, and everything we do has the aim of helping you learn. We’re starting small, with only problems and solutions for one class, Calculus I. That’s on purpose, so we can learn from you what works well and where we can improve before we create more. Please let us know: How are we doing so far? What should we do next? Please help us learn how to help you learn well!