FAQ: Remembering What We Learn

Mother and son working on math homework

“When we do our daily lessons, my son does great. Everything seems to click. But when he sees the same topic later, in a review or on a test, it’s like he’s never heard of it before. How can I help him pull math up from the dregs of lost memory?”

This is a common problem, and there’s no easy answer.

You see, it’s easy for humans to convince ourselves we understand something when someone else explains it. It seems to make sense, but it doesn’t stick in our minds.

If you think of times when you’ve tried to learn something new, you can probably remember the feeling—you thought you had it, but then when you tried to do it yourself, your mind went blank.

So how can we help our kids when they can’t remember what to do?

Continue reading FAQ: Remembering What We Learn

Charlotte Mason’s Living Math Launched: Order Your Copy Today

dad helping girl with math homework

And so it begins: Charlotte Mason’s Living Math is LIVE on Kickstarter!

Check It Out ❯

⭐ Don’t delay! ⭐

To have a successful campaign, we need plenty of people to back the project early. The more supporters we get in these early days, the more likely the Kickstarter platform folks will help spread the news for us.

Continue reading Charlotte Mason’s Living Math Launched: Order Your Copy Today

Coming Soon: Charlotte Mason’s Living Math

Charlotte Mason's Living Math Kickstarter

Coming Soon! In March, I’ll be launching my newest book, Charlotte Mason’s Living Math: How to Apply the Principles of Education to Help Children Develop Mathematical Reasoning.

And the Kickstarter prelaunch page is now live. That means you can sign up to get an email from Kickstarter as soon as the campaign launches:

Visit the Prelaunch Page ❯

(If you back the campaign on launch day, that encourages the Kickstarter folks to share it with more people.)

Continue reading Coming Soon: Charlotte Mason’s Living Math

Homeschool Memories: Bill Gates Proportions II

Woman on a shopping spree to buy books

Once upon a time, when my kids and I were young…

Later the same year, not too long after our discussion of the Bill Gates proportions, I stumbled on some more data. I discovered that the median American family’s net worth was $93,100 in 2004, most of that being home equity.

This gave me another chance to play around with proportions. And since I was preparing a workshop for our regional homeschooling conference, I wrote a sample problem:

The median American family has a net worth of about $100 thousand. Bill Gates has a net worth of $56 billion. If Average Jane Homeschooler spends $100 in the vendor hall, what would be the equivalent expense for Gates?

In the last post, I explained that a proportion sets two ratios equal to each other, like equivalent fractions. Each ratio must compare similar thing to similar thing in the same order.

In this case, we are interested in the ratio “Expense compared to Net Worth.”

Continue reading Homeschool Memories: Bill Gates Proportions II

Homeschool Memories: Putting Bill Gates in Proportion

Money Bag, dollar banknotes and stacked coins on wooden table

Once upon a time…

We were getting ready for the annual homeschool co-op speech contest, and a friend emailed me for help.

“Can you help us figure out how to figure out this problem?

    “This is related to C’s speech. I think we have all the information we need, but I’m not sure:

      “The average household income in the United States is $60,000/year. And a man’s annual income is $56 billion.

        “Is there a way to figure out what this man’s value of a million dollars would be, compared to the person who earns $60,000/year? In other words, I would like to say—$1,000,000 to us is like 10 cents to Bill Gates.”

        We found out later that her son’s numbers weren’t exactly right. He hadn’t understood the difference between income and net worth, so he made Gates sound richer than reality.

        But the basic math principles never change, and it’s fun to play with big numbers.

        Continue reading Homeschool Memories: Putting Bill Gates in Proportion

        What Is Math Game Monday?

        Learn a new math game every week, for free

        There’s a new Math Game Monday this week.

        Have your kids tried it yet?

        This week’s game is one of my favorites for upper-elementary and middle school students, offering plenty of practice doing estimation and mental math with fractions. Or you might prefer last week’s game, featuring a classic two-player logic puzzle that develops strategic reasoning.

        Or, if you’re reading this post later and missed those, there’s another great new game this week for you to play.

        Check it out:

        Visit Math Game Monday

        Continue reading What Is Math Game Monday?

        Musings: Math is Communication

        Young boy writing math expressions

        The question came up on a homeschool math forum:

        “My first grader and I were playing with equivalent expressions. We were trying to see how many ways we could write the value ‘3.’

          “He wrote down 10 – 2 × 3 + 1.

            “When I tried to explain the problem with his calculation, he got frustrated and didn’t want to do math.

              “How can I help him understand order of operations?”

              [If you think this sounds like too complex of a math expression for a first grader, you may want to read my blog post about math manipulatives and big ideas.]

              Order of operations doesn’t matter in this instance. What matters is communication.

              The mother didn’t know how to read what her son wrote.

              He could help her understand by putting parentheses around the part he wanted her to read first.

              He doesn’t need to know abstract rules for arbitrary calculations, or all the different ways we might possibly misunderstand each other. He just needs to know how to say what is in his mind.

              Continue reading Musings: Math is Communication

              FAQ: The Value of Math Rebellion

              Math Rebels fight for truth, justice, and creative reasoning

              I’ve been getting questions about my Math Journaling Adventures books:

              “I’m so excited to try math journaling! We bought your Logbook Alpha, and my 11-year-old math-averse son is trying to be a math rebel at every turn.

                “But I feel uncomfortable with the idea of rebellion. Doesn’t he need to learn how to solve math problems the right way?”

                One of my favorite things about math is that there really is no “right” way to solve math problems.

                As I pointed out in my ongoing Mental Math series, even a problem as basic as 6+8 can be approached from many directions. So perhaps I should say, the “right” way is however the student wants to make sense of the problem.

                In math, sense-making and reasoning are always the most important things.

                Continue reading FAQ: The Value of Math Rebellion

                Mental Math: Do’s and Don’ts

                Father and son working on math homework

                Over the course of this series, we’ve seen how mental math relies on a child’s own creative ways of thinking. In mental math, children develop understanding of how numbers interact with each other in many ways.

                In this way, they learn the true 3R’s of math: to Recognize and Reason about the Relationships between numbers.

                And the principles that underlie mental calculation are also fundamental to algebra, so that flexibility and confidence in mental math is one of the best predictors of success in high school math and beyond.

                But as we went through the various example problems, did you find the written-out calculations hard to follow?

                Don’t force your children to write down their mental math. It looks dreary when I write the calculations out step by step, but that’s not how it works in a child’s mind. With regular practice, this sort of thinking becomes second nature.

                Continue reading Mental Math: Do’s and Don’ts

                FAQ: Playful Math Journaling

                Girl student thinking about her math journal prompt

                Ever since the school year started, I’ve been getting questions about how to use my new Math Journaling Adventures logbooks.

                [SIDE NOTE: These logbooks are included in this month’s Thanksgiving Sale! You’ll get an automatic 10% discount off all print books, applied at checkout, no special code required.]

                “I love the way your math books get my children thinking.

                  “Finally, they are having fun with math!

                    “But sometimes I have no idea what the journaling prompt is all about or how to teach it. Where can I buy a solutions manual?”

                    Um, that’s not how math journals work.

                    The cool thing about journaling prompts is that they have no “right” answer. They are explorations into different parts of the world of math, nature walks in the land of numbers, shapes, and patterns. Springboards into whatever our children want to investigate, whatever sparks their interest.

                    A few of the problem-solving prompts may have specific answers, but it really doesn’t matter if our kids find the exact solution a math professional might give. If they write what makes sense to them, they’ve accomplished the goal.

                    If later, they think of something they hadn’t noticed, or they want to change their answer — well, that is mathematical thinking, too.

                    Continue reading FAQ: Playful Math Journaling