I love to write but on some days the words flow more easily than on others.

So many students resist writing and it’s often because they can’t get started. With them, and with myself, I try several approaches:

1. Brainstorming ideas and simply jotting them down as they emerge can help by getting those ideas out without worrying about the shape they’ll take. I tell my students that Step One is to locate your thoughts and Step Two is to worry about how artfully you express those thoughts. Keep those steps separate!

It’s quite surprising how many kids do a good job of organizing and expressing their thoughts coherently, once they’ve identified what those thoughts are.

2. The opposite strategy may also work: begin with a blank outline. I sketch the bare bones of a five-paragraph essay outline…

I. Introduction

II. First Point

III. Second Point

IV. Third Point

V. Conclusion

…and from here encourage the student to fill in as much as he can, in whatever order it occurs to him. Again, so much of what intimidates kids (and all of us?)  about writing is this feeling that what they write needs to come out perfectly right away. They don’t realize that writing is a tool for thinking and that it can start out sloppy and incomplete and disorganized and imperfect.

3. I’ve had a few kids who need me to write the first three or four words of the first sentence of their essay, and it’s as if that little start uncorks all the rest of their thoughts and they flow.

4. I love this trick from my writer friend, Jane: Pretend you are explaining your subject to one person, and write down what you “say.” Edit it later.

5. I recently discovered this last trick as I was preparing a presentation I’m giving tomorrow: Use your computer’s PowerPoint program. It has all kinds of outlining suggestions and templates. Brainstorm or write your outline or rough draft on PowerPoint, then copy it onto a Word document and finish up.

I love math and I could talk about it all day, every day, 24/7/365.  But I probably shouldn’t.  There’s so much more to the topic of learning than just math education.

So today I’m opening the second thread of my blog, which I am calling Curiosity Lane. It’s a place to talk about more general observations about the learning process.

My grown kids, Matt and Hannah, are here for Thanksgiving. I delivered them official warning that anything they have ever said or done as children, or will ever say or do from this point forward, is now potential blog-fodder….

…beginning with this thing I noticed as we prepared the meal: Wow! My kids are finally interested in learning to cook!

It’s true. During all their growing-up years I was in the kitchen pretty much by myself. There were the occasional bursts of enthusiasm for fudge-making or cupcake-decorating, but, otherwise, Hannah and Matt enjoyed eating but weren’t very interested in the process behind making meals happen.

But now that Matt’s out of college and living on his own and Hannah’s a college senior soon to be independent, they’re both motivated to learn to cook. And they’re most interested in preparing the foods they like, so Matt did the turkey and potatoes while Hannah made the carrot cake and the vegetables.

All the while they peeled and sliced and chopped and stirred, I was remembering my attempts over the years to cajole them into helping me out in the kitchen. Now here were these two energetic soldiers on active KP duty, eager for every bit of instruction, cheerfully performing every mundane task.

(It was, by the way, the most relaxed and delicious Thanksgiving I’ve ever had!)

There’s this old saying: When the student is ready the teacher arrives. We need to keep this in mind as we teach and as we learn. People are not blank slates waiting to be inscribed with knowledge. We all learn best when we’re learning things that make a difference in our lives. Subject matter that was boring or irrelevant at one point in life may be fascinating farther down the road, when it becomes important.

Matt does computer work, and …

My first holiday blog post…hmmm…how do I connect Math with Thanksgiving?

Well, on Thanksgiving we count things:  the number of place settings we’ll need, the shopping days before Christmas, and all the things we’re grateful for. Counting seems like a good topic.

Parents are thrilled when their child first gives evidence of  “knowing her nunbers.” Little Suzy has learned to count! And sure enough, four-year-old Suzy can point to objects and recite One, Two, Three…

But what does Suzy really know? What’s really going through her head as she rattles off these words?

It was during grad school that my brilliant professor, the author and Piagetian scholar Constance Kamii, drove home to me the difference between what kids really understand vs. what we adults assume or hope they understand.

If you’ve got a three-year-old handy (more likely as relatives visit over the holidays), try this:  Set out a line of about eight objects (M&Ms or buttons work well) and ask Suzy to count them. It’s very possible that she will lay her finger on each object at a time and announce ONE, TWO, THREE, etc.

Now, ask Suzy to “Please give me three.” And, often, Suzy will hand you the third object.

Many young children haven’t yet made the mental connections necessary to have formed the relationship we call “number.” Yet, they may have learned the names for numbers. For these little kids, number names don’t represent quantity; they’re simply names. Little Suzy might as well be saying MONDAY, TUESDAY, WEDNESDAY as she counts.

So when you then ask Suzy to hand you “three,” that’s what she gives you. She hands you the button whose name is Three.

Kids try their darndest to understand what we’re telling them, and many of their errors are funny and adorable.  Kids take in what we say, and then they use what they already know and what their brains are capable of doing, to make the best sense they possibly can.

And, really, isn’t this what we all do? Learning isn’t different for adults. We all try very, very hard to understand one another….and sometimes we “get it right,” and sometimes we miss the mark.

In his book, Lifelines, Forrest …

I’ve been tutoring math my whole life (since I was twelve! No kidding!…a topic for some other post), and I’ve never met anyone who couldn’t do math. It always seemed to me that the problem was not with the person, but with some preconceived expectation they were being forced to meet.

I met my own Waterloo in college calculus. I was used to the high-school pace of going to class every day for 50 minutes, and that daily dose of math instruction worked well for me. But now class met only twice a week and each class was two solid (VERY solid!) hours long. We covered five or six textbook lessons in each session. My brain simply could not handle all this.

And my freshman calculus experience was a cake-walk compared to my graduate-school statistics course. The class met once a week, from 6 to 10 PM. Imagine! After a full day’s work, there we doctoral students sat, laboring to absorb advanced statistics, for FOUR hours straight.  At 10PM we all staggered out like zombies. (My tutoring skills came in handy here; the textbook was pretty good and I was able to teach myself the material by working at it slowly, every day, during hours when I was awake and alert).

I’m a good student and I like math, but these classes just did not work for me. I find that I often need to adjust instruction to make it more brain-friendly. Whether you’re an adult or a kid, perhaps the math you’ve been getting isn’t right for you.

Our educational system is still structured on an outdated “blank slate” or “empty vessel” model of learning. It assumes that all people should learn the same material at roughly the same pace given the same instruction. We fill a classroom with same-age children (or we fill a college classroom with adults) and we expect them to receive and retain whatever material the teacher delivers.

Basically, we imagine the learners’ heads as containers into which knowledge is poured. Then, if learning doesn’t happen well enough or fast enough, we go looking for some flaw in the learner (perhaps a crack or a …

Many kids (and adults) struggle to learn math because classroom instruction isn’t enough to master this subject.

For one thing, math is cumulative.

• A student needs to master the earlier concepts before being able to understand the later ones.
• This means that if a kid falls behind the pace of the class he’s going to rapidly become more and more lost and confused.

Another problem is that becoming good at math requires active practice.

• Listening to a teacher explain math simply isn’t enough.
• Even if a student feels like she “gets it” at the time, she must practice on her own to really entrench that understanding in her head.

Five Tips for Coaching Your Child in Math

(Adult learners: Be your own coach, or help each other!)

1. Remind him that it’s hard work

I tell my students that their brains are going to do hard work and sometimes feel a little bit sore. That’s to be expected! Just like exercise, math requires effort and sometimes you have to push your brain and tire it out somewhat.

2. Enforce regular practice

Math should be practiced every day. On light- or non-homework days, go back and review concepts from previous lessons. Take hard problems and rework them a day or two later. If your child is struggling, she should be doing some math for at least ten minutes every day, even if it’s just reviewing the basics. It will get easier over time!

It’s no wonder that learning math is quicker or easier for some people than for others. In my last post we saw that math is not a natural skill. There’s no “math part of the brain” that automatically seeks out and absorbs algebra.

We learn math by painstakingly linking each new concept or procedure to what we already know. Our brains do this by building complex webs of connections between neurons leading to any number of brain areas. This process can’t happen overnight! We learn math one step at a time over many years. For some of us this process is relatively easy and enjoyable and for others of us it is more difficult.

Research in math learning reveals wide variations in the ages at which children acquire math concepts. For example, “multiplicative thinking” (essentially the child’s understanding of the concept of multiplication) has been identified in some children as early as kindergarten, yet is not present in half of all fifth graders!

Meanwhile, our educational system is still mostly structured on an outdated “one pace fits all” model of learning.  A classroom full of same-age children, all seated quietly and soaking in the day’s lesson from the teacher at the blackboard…this is such a lovely, simple, appealing image of the schooling process!  It’s too bad it doesn’t work very well for the learning of math.

Math, unlike most other subjects, is cumulative. You must master the earlier concepts before you can understand the later ones. Subjects like English and history aren’t like this;  you can study world history before or after American history and it won’t matter, but you won’t do well in algebra if your arithmetic foundation is weak.

In this respect, math most resembles foreign language study. If you’re not solid in  Spanish I you have little hope of doing well in Spanish II.  Other surprising similarities exist between learning math and learning a sport or a musical instrument. Mastering any of these pursuits requires a combination of instruction, regular practice, and individual and/or small-group tutoring. None of these skills lend themselves particularly well to classroom instruction.

So, at least one reason you or your child may find …

So many of us have negative feelings about our experiences learning math, and we walk around thinking of ourselves as “not math people.” And there is so much hype these days about math being easy and natural and fun for kids to learn, but then again we see so many of our children struggling.

Why, truly, is math so hard (let’s face it, it is!) for kids and adults alike? Part of the answer lies in our brain structure and the sorts of mental contortions math requires.

What makes the human brain so special is its ability to learn. This is why human beings have been able to inhabit every part of the globe and invent and create all the incredible technology and art we have produced. We are flexible innovators who can plunk down into almost any environment, and thrive!

Our brains are equipped to learn all sorts of skills that are not natural to us, including reading, writing, and mathematics. But that doesn’t mean these skills always come easily.

We are born with certain innate capabilities (vision and language acquisition are two examples), but then we are also able to learn many other skills by making neural connections between our inborn “brain centers.” We learn to read by rigging neural pathways from our vision centers (there are at least thirty) to our language centers.  (Braille readers link from tactile centers to language centers). We learn to write by building connections between vision, fine motor, and language centers.

And we learn math by making an even wider assemblage of mental jerry-rigs. Math, after all, isn’t a single topic. Arithmetic, algebra, geometry, calculus, statistics, discrete math; these are all very different pursuits. Depending on the kind of math we’re trying to learn, we will need to link in very complex ways to vision, spatial sense, temporal sense, quantitative sense, memory, language, and/or other brain centers.

Hunter-gatherer societies without formal systems of mathematics have words in their languages for “one,” “two,” “few” and “many,” suggesting that there’s a basic number sense that is inborn. Even newborns can tell the difference between small numbers like two and three; bored babies staring at a …

Doing the Math

This series of blogs is devoted to learning and mathematics.

Having said this, half of you are now on your way out the door…but please wait! We’re going to start by looking at why so many of us hate and avoid math, and why so many of our kids have trouble with this subject.

A Tutor’s Bread and Butter

True Confession:  I’m a math tutor, but I’m not “a math person.”

I’m much more of the literary, writerly, psychologist type. But because I tutor math people assume I’m a whiz, and often they ask me very hard math questions I then can’t answer, or they challenge me to calculate big numbers quickly in my head, which I also cannot do. They also exclaim that I must be musically inclined because don’t math talent and musical talent go together? I wouldn’t know since I’m gifted in neither.

Here’s what I am: Well-schooled, and well-practiced. I promise you, I know my math inside and out!

But it didn’t come easily.

In my line of work, math is where the jobs are. It’s my bread and butter. Algebra pays the rent, geometry buys the groceries, fractions have put my own children through college. I’m qualified to tutor in reading, writing, science, history…but far and away, above all else, what do I teach all day? MATH.

Why is math so hard? What makes it so much more challenging than other school subjects? Why do so many people turn up their noses at it? Why can I, an unremarkable mathematician, nevertheless understand it at least fairly well…and teach it?…and enjoy it? Could math be taught significantly better in schools (thereby putting me out of business)? What can you do to help your child if she or he is having problems in math?

First things first: No, it’s not you. Math really is not easy. There is so much hype these days about math being simple and natural for kids to learn, but then again we see so many of our children struggling, and then we look at their homework and can’t do the stuff, either!

Let me assure you: The …

When I was in graduate school my advisor had this sign on his door:

Life is the Only Game Where the Object is to Learn the Rules

Isn’t this a great way to think about life?… As a challenging game in which we’re constantly figuring out the twists and turns?

By the time I enrolled in my doctoral program I had already been a professional tutor for over 20 years. I made my living (and still mostly do) as a teacher without a classroom.  I sit with one kid at a time, shoulder-to-shoulder, working together on math or writing or science or SAT questions. We meet at the library, or the bookstore, or the coffee shop, or at my favorite location of all, the kitchen table.

It’s the greatest job I can imagine.

Tutoring is so much more than just studying for a test or helping write a paper. One of the great things I get to do is help kids understand how their own minds work. Why is math so hard? What’s the best way to learn those vocab words? How can you stop making careless mistakes? Why do you need to learn this stuff, anyway?…and how can you enjoy it more and feel better about yourself?

My other love is, well, Love! I spent almost ten years as a relationship coach and dating service owner, and I remain passionately interested in relationship dynamics and helping people learn more about their partners and themselves.

Learning is so much more than just this thing we do at school. Birds do it, bees do it… Rats and pigeons and even paramecia do it! People do it all day, every day, throughout life.

Every day my interactions with kids and adults teaches me some lesson, and I can hardly wait to share these things with you.

I’m excited to have this place to talk about learning and all its facets…learning and school, learning and work, learning and emotions, learning and relationships, Learning and Life.

Thanks for joining me in Always Learning!

Welcome to our new blog, Always Learning, by Leigh Pretnar Cousins. Always Learning is about how learning is a life-long journey, one that continues long outside of school.

Leigh Pretnar Cousins is a private tutor and test prep coach, with a masters degree in education and doctoral work in educational psychology and child development. Leigh also spent almost ten years as a relationship coach and dating service owner. This eclectic background makes her curious about many topics and the connections between them, and finds her writing about education, relationships, personality development and more.

I’m pleased to welcome you to this new blog, and hope you gain some nuggets of wisdom and learning yourself from the entries published here in the months and years to come! Please join Leigh in Always Learning!