Tag: learning math

  • The Prime Directive in Education

    The Prime Directive in Education

    The Prime Directive in Star Trek is to not interfere with other cultures.

    The Prime Directive in medicine is do no harm.

    The Prime Directive in parenting is to keep the child alive.

    There’s a Prime Directive in Education too!

    Through all my suggestions, recommendations and ideas about math education, the one thing that trumps everything else is the Prime Directive in education:

    If it works for your child, do it.

    If a method, book, course or person helps your child do better in math, then stick with it!

    Everyone has an idea of what great teaching looks like.

    Proponents of Khan Academy like that lectures can be available to everyone, everywhere for free. Opponents say that Khan Academy is still just lectures.

    Proponents of education methods popularized by Dan Meyer say that children need to connect with the math. They need to see it in action.

    Opponents (and there aren’t many) say that sometimes kids just want to do the steps.

    It’s not about great teaching, though — it’s about great learning.

    Only your child knows what great learning looks like.

    Children know how they learn best. They can’t always articulate it, thought, so they need us to watch them and figure it out for them.

    If your child needs more of a top-down understanding of what’s going on in math, then the teacher (you or the classroom teacher) should work to give him that.

    If he needs a to thoroughly practice the basics in math before moving on to something more — then that’s what he should have.

    Even alternative learning methods can be used.

    A friend of mine told me her child needs to practice his cursive writing. Because he thinks cussing and swearing is fun, she’s entertaining the idea of having him write sentences using a swear word. She worried that it might make her a bad parent.

    Enter the Prime Directive in Education. If he improves with his cursive writing, and she explains that swearing is still not appropriate out loud, why shouldn’t he write the bad words?

    If it works for your child, do it!

    Some kids need rote memorization before understanding. Some need understanding first. And some need bizarre means to connect with the task at hand.

    So if you find something that works — by golly, do it!

    What does your child need? How can you make sure he or she gets it?

    Share your thoughts in the comments or on Twitter/X.

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  • Is Math in the 3 Categories of Learning?

    Is Math in the 3 Categories of Learning?

    Our world is struggling with education of all sorts. We know that STEM fields are in trouble. Not enough people are excited about taking the science and math classes needed to jump into them.

    But there’s another piece of the education puzzle that’s missing — writing.

    I talked to a primary school teacher at a social function today. She was telling me how students these days were often taught the algorithms of writing. One of which is the classic intro-supporting paragraphs-conclusion that I remember.

    I said, “Oh, so they don’t get taught to write in their own voice, and stuff like that?”

    “That’s just it,” she said. “They naturally write in their voice. But with the systematic methods we push on them it destroys it!”

    That sounds familiar!

    It pulled on my heartstrings — there was another basic subject that was competing with the almighty and all-powerful queen of subjects — reading.

    Seems writing has the same challenges as math — people think there’s a formula to it when really it’s about voice, personal preference, beauty and art.

    And writing, like math, is something people always do when they have to but rarely do just for fun.

    What do we learn — really?

    It made me really think about learning and teaching. All learning can be boiled down into one of three categories:

    1. Learning information (historical facts, spelling, times tables)
    2. Learning how to get information (reading, researching, googling)
    3. Learning how to give information (writing, speaking)

    Reading clearly has its place in #2, as does writing in #3.

    But where is math?

    When you teach math, are you only teaching facts (like in #1)? Or are you teaching children how to get or discover information (#2)? Or are you teaching them how to give or share information (#3)?

    I’ll leave my answers for next time. Until then — what do you teach?

    Share your thoughts in the comments or on twitter/x.

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  • Differentiated Instruction

    Differentiated Instruction

    I just learned what the phrase “differentiated instruction” means. Jeanette Stein told me on #MathChat that for her, differentiated instruction is

    Meeting kids where they are at to take them where they can go.

    I love it!

    So I read the article Jeanette shared from Teach-ology. Seems differentiated instruction is a fancy term for focusing on the individual students rather than the teacher.

    I’ve been doing it for years!

    The first few semesters I taught math (back in 1996), I would lecture. I mean straight up, lecture. But soon I learned that it wasn’t about me.

    Over the next 16 years I watched the students. I quit spending so much time and energy on preparing lectures and much more time and energy thinking about the comments and questions I got from the students.

    I learned how students get quickly confused by the simplest of things – like solving an equation in one variable with four terms.

    I learned that the way something is said is much more important than what the words are.

    I learned that many of the “math rules” were merely tricks some clever person thought of as a mnemonic device. And that if these tricks are forced on certain students, they’ll likely never understand what’s really happening.

    The biggest trick/hoax is PEMDAS or the Order of Operations. Other math rules that get highly confusing are the Zero Product Rule and cross-multiplying (a term I personally despise).

    And most importantly, I’ve learned that creating a safe and inquiry based learning environment is the key to differentiated learning.

    And there’s more!

    In considering my classroom experiences, I’m finding many other instances and examples of differentiated instruction. So this is the first in a series on tactics to improve your own differentiated classroom. Here are the proposed topics/titles:

    • Eliminating the Fear – How to Engage Students without Calling on Them
    • Show Your Work! – What’s up with that?
    • Grading in a Differentiated Classroom – Why Teaching Math Is Harder than Giving Birth
    • “It’s Your Education!” – How to Empower Your Students
    • If Shakespeare Taught Math – How to Use Metaphors to Teach Math
    • If Picasso Taught Math – How to Use Drawings to Teach Math
    • How to Teach Your Students to Think Like a Mathematician

    Wow – that’s rather ambitious of me, isn’t it?

    I’ll shoot for these once a week and you can find a link to the series (this article) in the sidebar under “Quick References.”

    If you have any requests or ideas, let me know in the comments. And don’t forget to share this series with your PLN on twitter!

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  • How to Tell if Your Child Is a Top-Down Learner

    How to Tell if Your Child Is a Top-Down Learner

    Does your child struggle when you put him down in front of his math book? Are you frustrated in your attempts to get him to do math classwork or homework?

    Maybe he’s a top-down learner. If so, you might not know based on his current “regular” work. It will help in his education if you know he needs the big picture before the details – or the big theories before the steps.

    I remember learning to do derivatives when watching the foster kids that lived with us. I was eight. I’m a top-down learner. Here’s how to find out if your child is one too:

    How the “green beans” con works.

    My mom used to leave green beans open in a can on the table. We would walk by and eat them. If she put them on our plate, we would refuse them. So she got us to eat vegetables without asking us to, by just making them available.

    You can use the “green beans” con as a test.

    For math, put out the harder stuff. Find some books at Half Price Books or someplace cheap in your area. Open up the book. Sit and do some of the math yourself while mumbling aloud. Then walk away.

    If he sees his folks (or older sibs) working through those problems, he might be interested. Watch to see if he goes up to the book to check it out (steal a green bean). Be available to answer questions if he asks.

    If he can grasp some of  that “higher level” stuff, he’s probably be a top-down learner. He won’t want the building blocks until he sees the plans for the whole house. This could be the cause of some of the struggle and frustration – he’s been given the building blocks instead.

    Let him have the big stuff – start “allowing” him to do more of the advanced books. He’ll back up on his own to learn the “lesser” stuff so he can understand the big stuff better. You won’t have to force the work on him anymore.

    Share your experience with your top-down or bottom-up learning in the comments!

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  • The Real Place Kids Learn Math

    The Real Place Kids Learn Math

    Where did you learn math?

    I’ll bet the first answer you have is, “in school.”

    In my recent research of different types of math teaching, including dancing, literature and gaming, it’s occurred to me that I didn’t learn math in school. I learned arithmetic, I learned algorithms, but math?

    I learned math at home.

    My dad is an engineer, and by nature not a teacher. But we did puzzles. Cryptograms from GAMES magazine, computer-based role-playing games and TV-based video games. He wasn’t one for shoot-em-up or beat-em-up games (although swords were essential). Everything we did had logical thinking.

    My mother was an English major. She encouraged memorization of both prepositions and multiplication facts. And she played word games with me.

    Puns have a special kind of logic to them. As she was punning around with me, I was learning a unique set of skills.

    Of both of them, I was allowed to ask questions. Any questions. And I did. And they answered them.

    Everyone learns math at home.

    As a parent, your daily actions impact your child mathematically. It’s not your skills with pencil and paper that help you teach math, but who you are.

    You connect with your children and understand them because of your similarities to them. Remember how you learned math. Not how you learned arithmetic and algorithms, but math. The art of math.

    That’s your key to helping your kid learn math.

    How did you learn math? Can you use this to help your children? Teachers – how can you help parents tap into this side? Share your thoughts in the comments.