“Data demonstrates that those who are independently educated generally score between the 65th and 89th percentile on [standardized tests], while those in traditional academic settings average at around the 50th percentile. … Yet surprisingly, the average expenditure for the education of a homeschooled child, per year, is $500 to $600, compared to an average expenditure of $10,000 per child, per year, for public school students.”
http://www.breitbart.com/Big-Government/2013/06/07/Report-Growth-in-Homeschooling-Outpacing-Public-Schools

If you’d like to homeschool, I can help you with that. Even if you don’t know algebra, even if you think you can’t afford it, even if both parents work. Where there’s a will, there’s a way, and I’d love to help you find it!

Christine Stratton wants us to know that the public schools are not broken. She’s right. Our schools do exactly what they’re designed to do: place the same expectations on all students, regardless of how different they are.

In early elementary, students who don’t develop skills according to the prescribed timeline are labeled, and placed in a special class, and may never have the opportunity to catch up. In later years, students whose interests and talents diverge from the standard curriculum are pressured to go along with the system, whether or not it helps them toward their personal goals. Students who can’t learn effectively in the standard academic environment receive low grades that don’t reflect their true ability. Alternatively, if those students have a label, they receive special accommodations and an unspoken message that they’re less capable.

Whether for enrichment or assistance, every student I work with has needs that aren’t being met by the public school system. Realistically, such a large organization can’t be all things to all students, and that’s why so many people support charter schools, vouchers, or tax credits. We need to find a way, within the financial constraints we have, to allow for a variety of learning environments and let families choose what’s best for each student.

Some notable quotes:

“I left school at the age of 17 after deciding that I’d had enough of my school district’s attempts to forcibly shift my attention toward the classroom, and away from my independent studies.”

“Their job was to figure out what was wrong with me, to completely disregard the dangers of a confirmation bias, and to have me somehow classified for special-education. … I was placed in a ‘supplemental’ class where I could do my homework during school hours, and was placed on Adderall (an amphetamine) at 9 years old.”

“I was always told that I had potential, but because I wasn’t doing the work that they provided, I wasn’t living up to that potential.”

“I still knew I was gifted in some way, but felt that I was broken in every other way.”

” They … concluded that I was “emotionally disturbed”, which is not a legitimate term in psychology – it is an umbrella term invented exclusively for the purpose of placing severe classifications on students who can not be diagnosed with an actual severe disorder.”

“My school had wasted my time until there was no time left.”

If you believe traditional school is not providing the best possible education for your child, please contact me. I can help you consider which of the alternatives might work for you.

I realized that most of math class was “monkey training” and I became determined to challenge students to a deeper understanding. I read books and articles about how we think and about unconventional methods of problem solving. I thought about my learning experiences over the years, and experimented while tutoring.

Then I started teaching at Chippewa Valley Technical College. Because of tutoring, I taught interactively. I wanted every class to be a conversation and an exploration. Unfortunately, my ingrained expectations of what schools and teachers should be interfered with developing my own style. I felt awkward being an authority figure over adults.

My first semester teaching, the older teachers said, “Trade students are stubborn. They won’t do anything unless they see how it will help them earn money.” They told me not to justify topics, but simply insist “It’s required for your program.”

By the end of the semester, I had decided trade students actually have trouble understanding if they can’t see how a topic relates to the real world. Then I went to a professional development seminar. And heard about contextual learning. And thought, “Egads, I was right! I’m not the first person to realize this!”

But even then, the only way I knew to be more contextual was to make up realistic word problems and use analogies to explain math rules. I wanted to help my students really understand math, but something wouldn’t click. I encouraged them to take risks, but other teachers and department policies made me hesitant to take risks myself.

At the end of my second semester, I had a week-long class on teaching methods. I dreaded the thought of sitting still for eight hours a day, four days in a row, cramming so much into my brain in a short time. I worried that I’d have to write a paper, and that the class would be graded.

To my great surprise, that class was exactly what I needed! The teacher, Deb Walsh, broke all the rules and told us it to do it too! She told us to form a partnership with students rather than pull rank. She told us to minimize lecture time and maximize opportunities for students to take responsibility for learning. She told us to quit blaming and punishing students for their natural reaction to the school environment. She told us to get students out of their seats, encourage community, and make our classes a positive, exciting experience. She proved that students would do more and better work, voluntarily, if we changed the whole system. She proved it by using us as a demonstration.

During the week, I was mentally overloaded and did less than half of the recommended reading. But Deb didn’t care, or maybe she couldn’t tell. I was so involved in processing these revolutionary ideas and thinking of ways to make the most of these new freedoms, I couldn’t take in any more.

The last day of class, Deb invited us to each write something on the whiteboard to sum up our experience that week. I wrote:

I have permission to be creative
and sing in class
and quit trying to act tough.
(I’m not very good at that.)

And I told her about a blog I had just discovered, and Standards-Based Grading.

I haven’t had the opportunity to teach in a classroom again (CVTC is as-needed), but I’ve been getting more unorthodox with every student I tutor. I’ve discovered more great teacher blogs, and I dream of starting a totally outside-the-box non-school where I would be more of a facilitator while students teach themselves.

But in the meantime, I have a lot to learn!

I tried it out, and this is by far the most complete representation of algebra rules I’ve ever seen on a computer. It rivals the Algebra Models I wrote about before. It makes algebra so easy a five-year-old can learn it. And kids love the game — it’s more popular than Angry Birds on the AppStore.

There are a few relatively minor details I’d change, and I suggest you learn about the balance model of algebra along with playing DragonBox. But if you’ve had trouble with algebra, or if you’re a parent who wants your kids to avoid having trouble with algebra, DragonBox would really help.

Download it for Android, Ipad, Iphone, or Mac. If you don’t have one of those, there’s a web version available until the game is ported to PC.

But that’s not always true. Some topics in math class seem to come out of nowhere, wedged in the middle of some apparently unrelated stuff. Teachers know it’s because they’re considered necessary preparation for future topics, or because they’re considered important even though they’re not directly related to the rest of the semester. Unfortunately, most students have given up asking why.

Possibly the best example of an awkwardly wedged-in topic is Order of Operations. Sure, we all have to agree on a standard set of rules for operator precedence. But there are good reasons for these rules; they’re not just convention.

Unfortunately, the rules look totally arbitrary, because of timing. We teach them as a prerequisite to algebra, so students have no basis for understanding them, so all we can do is fall back on convention. We claim that math is logical, but the way we teach isn’t very convincing!

I propose that we simply skip the section on order of ops. The first time students need to substitute numbers for letters, talk about terms. When you find the area of multiple rooms, first you need to find the area of each room, then you add the areas together. Terms are like rooms: 2x is a term, and -3y is a term, and before adding them together, we have to resolve them. The fact that a is closer to 2 than it is to anything else provides visual reinforcement. Division is usually written as a fraction, so if z is on top of 2, clearly that must be resolved before adding 4. This covers the MDAS of PEMDAS, and for now, I’d leave it at that.

When we get to distributive property, I talk about parentheses being like a picture within a picture, or a story within a story.* If you want to multiply the picture by 3, you have to include the whole picture. So you need to either resolve everything within parentheses before doing anything else with it, or you have to be sure to include everything. Of course, resolving should be preferred whenever possible. I also remind students that their calculator can’t see how long a fraction bar is, so sometimes they need parentheses on the calculator when they don’t on paper.

Finally, when we get to exponents, I explain repeatedly that x, x², and x³ are like length, area, and volume. You can’t add 5 ft + 3 ft²; it doesn’t make sense. When you substitute numbers, you need to resolve the exponential terms down to just numbers, before you can combine them. Any operator only applies to what’s right beside it,** so 2x³ means 2 cubes or 2xxx, not (2x)(2x)(2x).

In my experience, most students see math as a labyrinth of inscrutable rules. No wonder they hate it! This way of presenting order of operations flows with the rest of algebra — students won’t even think about memorizing because it will just make sense.

This idea developed gradually when I taught a very basic algebra class. I refined my plan in response to two posts by Timon Piccini at Embrace the Drawing Board. Do you see any problems with this? How would you improve on it?

* I just thought of this analogy while writing, and I like it better than my previous explanation.
** Yes, this is also true of addition and subtraction. They only act on the result that’s right beside them, when it’s their turn to act.

I strongly recommend the book to anybody, but I must warn you, if your kids are headed for school in the fall, you’re likely to change your mind at the last minute.

Call me to discuss inexpensive options. The evaluation is always free, and you may not need ongoing tutoring. You can homeschool your children!

I learned about Kristi when somebody sent me her weekly newsletter. The issue I read, titled ”Lies My Union Told Me” is an excellent rebuttal of the five main talking-points she’s heard from her opponents. Considering all the complaints I’ve heard about teachers and school budgets, I think a lot of students and their parents will appreciate this article.

Discouraging questions is stupid. Teachers feel pressure to “get through the material” and many don’t know how to cope with unscripted exploration, and 30 brains thinking 35 different thoughts. But when students ask questions, it means they’re ready to learn something. That’s a golden opportunity! It doesn’t happen on schedule, but it’s the whole point of teaching!

Expecting everybody to learn the same way, at the same rate, is stupid. We come in all shapes and sizes, with all different interests, experiences, talents, and struggles. Since our lives are so different, doesn’t it make sense that our thought processes and mental habits are different? When a student doesn’t understand a teacher’s explanation, why do we assume the student is deficient in some way?

Expecting students to sit still and listen while the teacher talks is stupid. Students need to get involved in what they’re learning, not just copy the teacher’s example and try to imitate later. At best, that produces trained monkeys who don’t know what do to when they see a different type of problem. And in the real world, all the problems are different.

Expecting everybody to do the same homework is stupid. Some students need to do lots of examples. Some need to do just a few, but need to really think about the principles. Some need to draw pictures. Some need to prove the theorem for themselves.

Teaching new material when students haven’t understood the previous topic is stupid. Math, more than any other subject, builds on previous material. It’s better for a student to learn less, but learn it well, so they can actually use it.

If you’ve struggled academically, maybe you learn differently from the way most teachers teach. Maybe you missed a fundamental concept that everything else depended on. Maybe you can’t remember the information because you don’t see how it relates to anything. Maybe you had a bad experience that left you feeling like a failure.

None of that makes you stupid. You can take the initiative to figure out how you learn best, ask questions until you get satisfactory answers, and study the topics most relevant to you. And I’d love to help point you in the right direction!

Some guys actually expect to be called by their last name. This is a completely foreign concept to me.

Trade students are not lazy or stubborn, any more than the rest of us. (I’m talking to you, fellow teachers!) They honestly have trouble understanding the material when they can’t see how it relates to the real world. Learning in context is actually more effective for all of us.

Assigning homework over a break is pointless. Nothing I can say will get them to do it.

When I made big mistakes, other teachers told me men don’t hold grudges and the next day they’d be fine. Actually, some men do hold grudges.

There are lots of intelligent people who have trouble learning from books and lectures. (I already knew that, but it bears repeating.) They often think they’re not too sharp, put themselves down, and have low expectations for themselves academically — this causes a vicious cycle.

Sometimes I’m an example of the kind of teacher I’m trying not to be.

Saying, “Knock it off!” in the right tone of voice solves a multitude of problems and is a great knee-jerk reaction to cultivate.

The Look (the one I inherited from my mother) can scare a macho 18-year-old guy. That really surprised me.

Students who think concretely have no framework for understanding anything theoretical. Talk about a general equation, and they’ll be like deer in the headlights. Put numbers in the equation, and it all makes sense to them.

I’m as impressed by practical skills, as other people are with academic skills.

Trade students tend to be hands-on learners – that’s why they chose to learn toolmaking instead of marketing. Next time I’ll use lots of manipulatives and give them plenty of opportunities to move around. No more sitting in a chair for an hour.

Trade students tend to be … rough around the edges, but once I got used to them, they were some of the most exciting people I’ve ever taught. I can’t wait for the next opportunity!