| Questions | Answers |
|---|---|
| Why do so many children (and adults) hate advanced math? Is it how it's taught, or what is taught? | It's a deep question, and I'd like to warn that the answer is somewhat disturbing in its implications. Yes, some of it is WHAT is taught - the number crunching without patterns, the primitive yet tedious topics instead of beautiful adventures of the mind, medieval content not linked to current trends. The "what" part is relatively easy to address: there are wonderful materials out there! Innovative books, cool computer simulations, hands-on construction sets, etc. |
| And a part of the problem HOW math is taught: we do need to mind what we know about human learning, such as spaced repetition for memory, the power of multiple examples that come from your peer group, the motivation of making mathematics your own. | |
| Yet the most difficult part that tends to stay off-screen is WHY math is taught. Advanced math is taught as a gatekeeper, as a means not to starve. It trickles all the way down - I hear parents of children as young as five or six say that if they don't push math now, the child will fail forever. To quote a presentation: "Why do we need to know multiplication? One reason is that multiplication is on many tests kids take. The story goes like this: if kids don’t know multiplication facts, they will fail tests, which means they won’t get into college, which means no career, which means epic fail of the whole life. For want of a nail, the kingdom is lost." | |
| So people hate math because they learn it out of fear. How can we help kids learn math for meaningful, joyful, loving reasons? That's what it's all about... | |
| So fast forward a couple of years, and I discover (to my horror) that I had a problem that required the real-world application of calculus. So I dragged out my old textbooks to review. | At Natural Math, we have "math sparks" for each topic we introduce to children - you can check out a couple of calculus sparks on this page, and see how they start with whys: Link to naturalmath.com |
| What books would you recommend to someone who sucks at math ? | It's a very broad question, because no person can suck at ALL math - there's too much of it! I am yet to see anyone who hates math art, programming, hands-on modeling, problem-solving, social justice statistics, the sixty-three major math subject areas - all at the same time. |
| So, what do you like, what are your hopes and dreams? What books do you like? Or maybe it's not a book, but a game or a movie? Let me know. Meanwhile, here's a site I respect for book reviews: Link to livingmath.net | |
| Ok, I get how a 5 year old could probably understand limits but please explain to me how the average 5 year old can understand differentiation and integration? | First of all, let's be clear that a 5yo can understand the concept and idea of limits or integrals, but probably not computations of them from something like AP Calculus test. It's such a FUN task to ask yourself - how can I help a little kid to play with derivatives? And to figure it out! A lot of it is in storytelling and hands-on play. |
| Zeno's paradoxes or Hotel Infinity stories are perennial favorites for finite and infinite limits: Link to en.wikipedia.org | |
| Here are our hands-on activities for integrals and derivatives, from the Inspired by Calculus course. They have particular examples. | |
| Integration as 3D printing, layers on an onion, LEGO building - "What Would 3D Printer Do?": Link to drive.google.com | |
| Integration as mosaic, beads, pixel art: Link to drive.google.com | |
| Integrals and derivatives in "X-ray vision" metaphor - making flipbooks! Link to drive.google.com | |
| I hope these examples help to get started. There are more, like this interactive toy for beautiful rotations - kids love it: Link to www.zefrank.com | |
| What do you think would be the best components and concepts of an interactive math learning game targeting both children and adults? | This is a large question. I am so tempted to just spend the next hour on this :-) Any concept in math is someone's baby - some people worked it out with love and care. So, any math topic or problem - Euler's formula, geometric series, knights and knaves puzzle - can be INTERESTING. However, some are more POPULAR than others, and some are more CENTRAL to other topics. |
| If you pick a popular topic, it will be more memetic and easier to share with others. For example, fractals. Everybody loves fractals, it seems. They are in the main song in a Disney movie (Frozen). They go around a lot on social media. So if you make a game about fractals, people will probably relate to it - both children and adults. | |
| You can also study what hang-ups people have in math, and target those. If you make a game that teaches people the deep calculus issues related to .999...=1, I bet both children and adults will be thankful! We worked out a hands-on model for this one, where children cut squares or triangles (into smaller and smaller pieces) and then reassemble them back into the whole thing. | |
| Can any of your research and methods be used to help adult learners gain confidence and skill in calculus or is it something that would work only for young children? Thank you! | Secretly, all Natural Math methods are for adults too. (Well, it's not really a secret, just something my colleagues like to joke about.) People feel that if a method is gentle, playful, accessible enough for five-year-olds, they might give it a try! Children are like pied pipers, leading their grown-ups to give math another chance. |
| Some people even "borrow" children for the purpose: a niece, a friend's child, or a group at a math circle. | |
| What grown-ups say: "I've never thought of it that way - never linked integration and topo maps, but now that we made them out of foam, it's so obvious!" "I come to the math circle for my child, but it's so fun and therapeutic for me. I play for my own sake." | |
| If activities are deep, easy, and playful, grown-ups find them valuable too. Math anxious people find it therapeutic, and professionals in math-rich fields find new inspirations. | |
| How do you feel about teaching young children proofs? I sometimes feel that my early math education would have been easier if I had seen proof of the methods/equations we were using, but I'm not sure if that's just some kind of bias since I now have a degree in a subfield of applied math. | I am all for helping children see WHYS. Why does the quadratic formula give us solutions? Why have people bothered to invent limits? Why does the Pythagorean Theorem always work? I love to work out child-friendly whys behind more advanced topics, like complex numbers (carousel around the axes) or integration (assembling blocks in Minecraft). |
| And also, logic and rhetoric and paradoxes (topics related to proofs) are both accessible and fun for young children. We have a book out called Camp Logic, and people report good results with it: Link to naturalmath.com | |
| You are right about bias, though. Some people, including children, are much more interested in building, modeling, or artistry in mathematics - the HOW of it rather than the why. So, the proofs and whys should be there, and accessible, but as one venue of exploration among many children can choose. | |
| Do the majority of parents that seek out your expertise do it in order to be a partner in their children's education, or are they more of the "tiger mom" type of parent that pushes their children to be exceptional? | Natural Math focuses on adventure, open problems, and explorations; such activities don't give direct immediate advantage in very competitive situations. The type of parent parodied in the "Tiger Mom" novel (and it was satire, by the way!) seeks ways for their child to win (over others). I don't see that pattern of behavior in our community - it's very collaborative. Parents and teachers doing Natural Math tend to be awesomely nurturing and supportive, of their own children and others. They may do some "tiger mom" stuff outside of our activities, but if so, I just don't get to see it! |
| Edit: Typo. | A lot of these parent behaviors are driven by fears. If the community and math activities are built on love and care and helping each person to be brave, people behave gently. |
| I'm a student finishing up my bachelor's in math, and I have a 12-year-old sister who's interested in math as well. She enjoys interesting concepts, but doesn't like actually solving all the algorithmic problems she's given in school. How can I best support her and show her the parts of math that she'll enjoy? | Hi MPREVE - there are several things to do that will help. One easy thing is to find cute, profound, cool math pieces that are easy to share, and send them your sister's way, maybe when you chat. Like these videos (just start with one you like): Link to www.youtube.com |
| You can also help your sister find a math circle, a robotics group, a hackerspace - any group that does math, science, and engineering for love, and that would treat your sister well. There are girl programmer groups and so on - look around, ask your sister what she loves, keep her involved in all decisions. If she connects with such people and enjoys the experience, it's a big huge step toward keeping your own values in learning (in spite of other, less meaningful experiences). | |
| What's the most important advice to give elementary school parents about how to help their children succeed in math? | Choice. |
| Whatever you do in math, arrange it so your child has three or more choices of that. Want to offer a problem? Have a selection ready, and help the child select problems. Learning multiplication tables by heart? Look at three or more methods (pattern-based, spaced repetition, number tricks) and help your child try them out, then pick what works. "Do you like algebra, geometry, or calculus more?" Well, expose your self and your child to other sixty large areas of mathematics, such as logic, topology, number theory - and help to choose the topics that speak to your child most. | |
| Help children make informed choices. | |
| Being 24 I remember graduating high school when technology was starting to enter the classroom. Everyone had cellphones, the Ti-89 calculators could solve derivatives and integrations for us; basically, technology was in the hands of all students and we knew how to use it to our advantage. | The decision on which activities are best "unplugged" and which are great with tech is always interesting. For example, integration with LEGO is a lot of fun in physical space - but Minecraft is great for the purpose, too. |
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