This letter is to students in college math classes, but might apply in other settings such as secondary math or other subjects.
Dear Student,
I am writing this letter to you, because your instructor, other instructors, all of us care. We care deeply about your success. We care about your future, and the future of others. That's why we went into teaching in the first place, a profession notorious for long hours, high commitment, and not the highest wages. Teaching is a calling, and our calling specifically is to help young people today to prepare them to solve tomorrow's problems. Teaching is a social responsibility to young people, to prepare young people with the knowledge, creative thinking, and values needed to live healthy, successful, impactful and meaningful lives.
Consider this next idea for a few minutes about time... Children who are in kindergarten today will retire in about 60 years. I write this in 2019, and that means a student in kindergarten will retire around the year 2079. 2079! Think of the difference between what your life is like today, compared to 1959. The world has changed drastically in ways that people in 1959 could not predict. No way they could foresee smart phones, google, climate change, automation, globalization, etc. The main point I want to get to is that there are questions and problems that young people (you) will have to solve that have not even been thought of yet by anyone on the planet. Your education today must prepare you to solve these unstated, problems far out into future.
What this means is that getting the answer in the back of the book isn't nearly enough. Yes, it's good to check your answers sometimes, but that's just a small part of your education. Yes, it might have worked to get you into college or through your last math class. I totally get it. But learning isn't a set of check boxes or getting the answer that is in the back of the book. The people who invented the iPhone or the people who put the first human on the moon or your favorite band or your pediatrician or whomever else you admire or appreciate, they solved real-world problems and looked far beyond the back of the book. At some point, logic, reason, and creativity is what you need. Answers might be good for checking things off, but really the learning is the process to getting to the answer and being stuck on good questions that make you think.
Let's unpack some of the details. It's okay to ask, "Is this right?" Please ask for help, and ask for help every time you need it, even for small questions. But I hope you also go farther, and ask questions that expand your thinking. "Why does this work?" or "Why doesn't this work?" or "Is there another way to look at this?" Memorizing isn't thinking, by the way. We can teach computers to memorize better than humans, and thus memorizing isn't as important as it might seem. Sure it might help you get back a multiple-choice test, but really in your future life multiple-choice tests won't be how we tackle something big like climate change. The big goals of your education include deep understanding, being able to explain complex ideas with nuance, being able to learn from others, and being able to use ideas creatively in new ways often collaboratively. Hence asking for help should be part of a larger process to make sense and expand your understanding and thinking. Learning is fun when it makes sense! And if it doesn't make sense, then keep on trying to understand and get help.
You can get help from various resources. Resource number 1 is your instructor. That's the person who is responsible to your learning. Next there are your classmates, your textbook, the tutoring center, and perhaps the internet. Try and talk to as many humans beings as you can first. Math is learned better with more human interaction.
Office Hours: Office hours are for you, and if you are stuck on something, even a small thing, go to office hours. It's not an imposition when you show up, and your instructors want to help you. Even if you instructor seems completely different than you, you can and should ask for help. While it might seem a bit scary, it's ok. I know a ton of math instructors, and so far all of them are human beings, and are really nice in office hours. Some even have a sense of humor! I know that might be shocking, but it's true. And when they go home, they go home to things like cats and children, and watch TV or text their friends about Friday plans, just like you.
Yes, there exist legends of math geniuses, who work in their attics for years to invent math. That works for them in certain contexts, but none of them worked alone or got to that point all by themselves. They have collaborators, consultants, books,... they actually went to school with other human beings at some point in their lives (and interacted with them). They read journal articles, they attend seminars, they go to conferences. Some people gave them a job, so opportunities were given to them. No one is 100% self made. Therefore, work with other people regularly, even if you don't view yourself as "social" in the everyday sense of the word or are introverted. In this letter, I mean social in a school or workplace sense. We all have to communicate with others to give and receive feedback, as well as brainstorm new ideas.
And really I hope you get stuck a bunch of times in your learning process (in a safe learning environment, not on tests). Get stuck??? Yes, get stuck. Because you need to push your personal abilities. Each time you get stuck and unstuck, you learn what works and what doesn't work and you get smarter. Through working on problem solving in math (or any field), you are doing something like going to the gym for your brain. Your brain will get stronger, and you'll learn new ways to think, see, and feel.
Math anxiety is a real thing. I've written about it many times on this blog. I've talked to hundreds of students about it. I'm sorry about this. Math anxiety should not exist. Not everything in the world is right, and math anxiety is one of those wrongs that we are trying to fix. In the meantime, if you had experiences that led you to math anxiety, what you need to know is that it's not your fault! You're not dumb, you're capable, and there is a way out.
The way out is doable. It's shifting from a fixed mindset (where one views their math abilities as fixed at birth), to a growth mindset, where one views effort and practice as the ingredients for getting smarter. Think about one of your hobbies or interests. How did you get better at it? You practiced. You might have had a teacher or coach or watched videos, but at the end of the day you put in the focused, dedicated hours, and did the work. That's being smart, and from now on, we are co-opting the word smart. Getting smarter at math is exactly same. A good teacher will provide you with a positive class environment and support you through your specific learning challenges, and when you practice, think, ask questions, collaborate, and do all those things people do in every profession and hobby, you'll make real progress.
Only watching videos of other people doing the math isn't going to cut it. Look I get it. Khan Academy is one click away. It's a useful resource, and I even watch KA sometimes to see which ones might help my students. Whenever I need to fix something in my house, I find a video on how to fix it. That's a good way to get information that you lack. However, learning math is like learning to be a musician or athlete. It's not just information and facts, but also about developing thinking and problem-solving skills. Doing better at math requires thinking mathematically, which is analogous to learning to ride a bicycle. You can't be taught to ride a bicycle beyond the basics by watching a video, because there are things your brain and body have to construct by actually doing it in order to build that skill. Mathematical thinking is the same in that you can't just get info uploaded into your brain like a firmware update. You also need to construct understanding and meaning for yourself, just like your body and brain have to construct things in order to ride a bicycle safely.
Another example is learning how to hit a baseball/softball. We could watch tutorials all day and understand what we need to do. Basically it's swing a bat and hit a ball. But only watching videos is obviously not enough. We need to actually swing a real bat and hit a real ball and get ongoing feedback from coaches. And then practice, play games, strike out, reflect, rest, repeat. It takes time to get good at it. That's the perspective you should have about Math and watching videos. Sure watch videos sometimes to get some info, but don't stop there. Start there, and do the work. Do your own reps on real problems. Otherwise, you'd just watching, and that is just sitting in the stands. You need to be on the field, because this is your life and your future. Get in the game!
Hopefully, your instructor will ask you to work with your classmates sometimes on a question or task. In education this is called active learning and is part of inquiry-based learning (IBL). These methods are designed specifically for you to engage and think for yourself. Listening to someone isn't enough. Sometimes we need to hear ideas from the instructor that we can't easily build ourselves, but like sports or music or any hobby, you ultimately need to be the one engaged in the process, asking questions, and taking ownership of your development.
Learning to work with others is critically important. Working in groups is not only about helping one another, although that's a good aspect of group work. One of the main benefits of group work is learning through discourse. Sometimes we need to talk things out in order to make sense of what is going on, and hearing other people's ideas can also benefit all of us, and helps us engage in the process of trying and refining new ideas. Another benefit of group work is learning to communicate. In an era when more and more repetitive tasks are being automated, the ability to do humanistic work, such as communication and problem solving, is much more important and valuable.
Try to contribute to group discussions and regularly invite your group mates to share... "So what do you think? What did you get? [smile]" It's not about one person getting the answer for the group, and everyone else copies. It's about giving everyone a chance to think, try, share, refine, and see ideas from multiple perspectives. That's good for you!
In summary, focus on problem solving as a process, embrace and be patient with being stuck and not having answers right away, think about the long game of your personal intellectual development, develop a growth mindset, and work on learning with your classmates. These are things you need to prepare for your future. All people, especially young people, have immense capacity to learn, grow and get a lot smarter! Believe in yourself by actively investing in how you learn.
Best wishes on a successful new school year!
Sincerely,
Professor Stan Yoshinobu
