Expert Advice from Ashley Cherry: Problem Solving
Rediscovering the Joy of Problem Solving
“I don’t know what I’m going to be when I grow up, but I know that I do NOT want to do math all day.”
--Ashley Ray, Journal Entry (6/12/2004), Age 14, just finished 9th grade
“I have my dream job. I love math and I love teaching.”
--Ashley (Ray) Cherry, (5/12/2020), Age 30, Math Professor
So, what happened to the girl who didn’t care what she did when she grew up as long as she didn’t have to do math all day? Two things.
1. “In his heart a man plans his course, but the Lord determines his steps.” --Proverbs 16:9 The scripture speaks for itself.
2. I rediscovered my love of math. I liked math just fine when I was young, but my love turned to hate somewhere in middle school. Later, I remembered why I loved it again (in the middle of an AP Calculus course of all places).
The truth of the matter is that we never really know what jobs or careers our students will end up doing or what skills they will need to know for the path they choose. Obviously, my middle school self had no clue what would lie ahead! If I had quit math at age 14, I would have missed out on discovering my dream job.
In this time of quarantine and social distancing, I know that many parents are struggling to remember the math they once knew (or the math they hated once they reached middle school). Perhaps you never loved math to begin with and now you are trying to help your kids add fractions or solve for x with much weeping and gnashing of teeth. Hopefully this list of resources and ideas will help you find a place to start. Who knows? You may have a math hater in your house that will grow up to be a math professor! Maybe you can help them discover that math can be fun after all.
Everyday Activities at Home: For younger kids who are still learning arithmetic, the possibilities are endless. At its best, math is a tool that empowers us to solve problems, puzzles, and mysteries. The next time you catch yourself doing some arithmetic, ask your kids to help. The most practical math we do is the math that is scribbled on napkins and receipts and in the margins of our lives, the math we use to make choices throughout the day. Galileo Galilei once wrote, “Mathematics is the language in which God has written the universe.” Help your kids open their eyes and look around. Math is everywhere. I’ve listed some ideas to help get you started.
In the Kitchen:
What recipe are you making? Let your kids pick from a list and help you make the grocery list and estimate how much it will cost.
Does the recipe make too much food or not enough? Try halving or doubling a recipe to help kids practice with their fractions. Tell them to check their work because if they do it wrong, you might have very salty cake or so much batter that it doesn’t fit in the pan. Math that results in cake and cookies is the best kind of math.
What about unit conversions? How many teaspoons in a tablespoon? Cups in a quart? Ounces in a pound? Can they pour water into different measuring cups to see what’s equivalent and what’s not?
That toy or game they’ve been wanting? How much money does it cost? What is their allowance? How many weeks will it take for them to have enough money to buy it themselves?
Can your kids calculate the tip for the pizza delivery guy before he arrives? What if you want to give him a higher tip?
Going for a walk? Look at the architecture. Do you see isosceles triangles or semi-circles? Are there right angles, acute angles, or obtuse angles? What might happen to a house over time if the angles aren’t correct and something isn’t level? Have them record their observations with sidewalk chalk.
Playing a board game? Let your kids take turns keeping score. Being the banker in Monopoly or the scorekeeper in Scrabble or Yahtzee provides great practice.
Check out Disney’s 1959 movie Donald in Mathmagic Land. It’s only 27 minutes, and it’s more entertaining than a math tutorial video. Better yet, watch Hidden Figures to see how mathematicians contributed to the Space Race.
There are so many amazing children’s books out there that teach kids math. Here are just a few.
Sir Cumference and the First Round Table (1st in a series of 9 books) by Cindy Neuschwander and Wayne Geehan
The Grapes of Math by Greg Tang
Math Curse by Jon Sciezska and Lane Smith
I’m Trying to Love Math by Bethany Barton
Hidden Figures by Margot Lee Shetterly and Laura Freeman
Pre-K to Early Elementary School: Check out the PBS shows Odd Squad and Peg + Cat.
Middle School / High School: Check out the CBS show Numbers for a lot of crime solving mathematical applications.
Free Online Math Activities and Games:
NASA Kids Club Website @ nasa.gov/kidsclub
PBSKids Math Games @ pbskids.org/games/math
PBS Parent Site for Developing Math Skills in Early Ages @ pbs.org/parents/learn-grow/all-ages/math
Desmos.com (has a free online graphing calculator)
YouTube Channels for Middle School / High School:
NancyPi: Created by an MIT graduate, this YouTube channel has tons of free tutorial videos for algebra and calculus help! If you have a middle school or high school student struggling with algebra or AP calculus, definitely check this out! This channel is my personal favorite because the videos are bright and cheerful and seem less dry than some lecture videos out there. I’ve suggested this resource for LCU students who need additional help as well.
Khan Academy: Khan Academy is a good place to find tutorials for any subject. For example, there is a Khan Academy algebra channel with 92 videos covering everything from middle school Pre-Algebra through high school Algebra II. If you’re trying to help your kid learn math you haven’t done in twenty years, this is a great place to look for help.
Websites with Tutorials, Lessons, and Practice:
Khan Academy: In addition to the YouTube channel, Khan Academy also has a website with notes and practice problems on any subject. I like that you can read through some examples and then try some multiple-choice problems to check for understanding. There are hints and step-by-step solutions, and every time you click refresh, you get a new set of randomly generated practice problems so you can practice as much as needed.
Purplemath: Free tutorials, lessons, and practice for everything from 5th-6th grade math through Algebra II (trigonometry included!)
MathPlanet: Free lessons for Pre-Algebra, Algebra I and II, and Geometry
A WORD OF CAUTION: There are tons of websites and apps that allow the user to input a problem (or scan a problem with their phone) and the app will solve the problem and provide step-by-step solutions. You may have observed that I purposefully did not provide those in my list of resources. If a parent chooses to download one of these apps to check their child’s homework, or if the student uses an app to check their work, these apps can be helpful. If the student, however, copies solutions off a screen all month long instead of working problems on their own, they might as well have copied twelve pages out of the Encyclopedia Britannica. They may learn a little bit, but they won’t learn anything very well and the chances of retaining that information when they go back to school the next semester are slim to none. These students have accidentally become scribes rather than problem solvers.
A WORD OF ENCOURAGEMENT: Research tells us that students learn better when they wrestle with a problem and then discover a solution. The moment of victory (that light bulb moment) is what propels them to try again, challenge themselves, and grow. When we provide solutions to a problem too soon, we rob them of the light bulb moment, and we may accidentally crush their interest in learning the concept. It’s as if you were in the middle of a book, and someone walked up to you and said, “SPOILER ALERT: Old Yeller dies at the end.” Why would I want to keep reading now?
Can helping kids with math homework lead to weeping and gnashing of teeth? I don’t deny it. It can be a love/hate subject even for college students (and dare I say, professors?) who love it. It’s always
frustrating to encounter a problem you think you can’t solve, but the joy comes when understanding dawns and you solve a problem you never thought you could. My one parting word of advice would be to let your kids wrestle with a problem a bit before you intervene. Some students wrestle longer than others but give it enough time and effort (and maybe another example or two) and the light bulb will come on. You will know your students (or kids) are learning when you pick up your pencil to help and they say, “Wait! Don’t help me yet! I want to see if I can figure it out.” As a teacher, that’s how I know my job is done. The most successful students in my classes are the ones who flat out refuse to give up. They are the students who pop into my office and say, “I spent so long on this one problem. Can you give me a hint? I don’t want to know the answer yet. I just want to get un-stuck,” and the students who run into my office beaming with pride and say: “I spent two hours on one homework problem last night, but I figured it out, Dr. Cherry!” The joy of math lies in the discovery that with just a little more effort, you can figure out something you initially thought was impossible.
As Albert Einstein once said, “It’s not that I’m so smart. It’s just that I stay with problems longer.”
Hang in there! The joy is in the challenge.
About the Speaker
Ashley Cherry is a LCU Assistant Professor in Mathematics