Secrets of the Colosseum

Beste and his colleagues spent four years using measuring tapes, plumb lines, spirit levels and generous quantities of paper and pencils to produce technical drawings of the entire hypogeum. “Today we’d probably use a laser scanner for this work, but if we did, we’d miss the fuller understanding that old-fashioned draftsmanship with pencil and paper gives you,” Beste says. “When you do this slow, stubborn drawing, you’re so focused that what you see goes deep into the brain. Gradually, as you work, the image of how things were takes shape in your subconscious.”

The Art and Science of Remembering

The Art and Science of Remembering

  • “When retention was tested immediately after learning, both napping and cramming produced better retention than taking a break, but only the nap benefit remained significant when tested one week later,” the researchers concluded.
  • The quiz was then repeated a half-hour later and again a week later, and in both retests, the people who sat and did nothing for 10 minutes “remembered much more,” the researchers reported in the journal Psychological Science.

Make Your Daughter Practice Math. She’ll Thank You Later.

  • For parents who want to encourage their daughters in STEM subjects, it’s crucial to remember this: Math is the sine qua non.
  • You and your daughter can have fun throwing eggs off a building and making papier-mâché volcanoes, but the only way to create a full set of options for her in STEM is to ensure she has a solid foundation in math.
  • Math is the language of science, engineering and technology. And like any language, it is best acquired through lengthy, in-depth practice.
  • You can begin to avoid practicing it, because to your mind, that practice is more painful than learning what comes more easily. Not practicing, in turn, transforms what started out as a mere aversion into a genuine lack of competence. Unfortunately, the way math is generally taught in the United States — which often downplays practice in favor of emphasizing conceptual understanding — can make this vicious circle even worse for girls.
  • When we learn to play an instrument — say, the guitar — it’s obvious that simply understanding how a chord is constructed isn’t the equivalent of being able to play the chord


The Scientific Argument for Mastering One Thing at a Time

  • In fact, researchers found that people who tried to accomplish multiple goals were less committed and less likely to succeed than those who focused on a single goal.
  • But here’s the thing: automaticity only occurs as the result of lots of repetition and practice. The more reps you put in, the more automatic a behavior becomes.
  •  After 30 days, the habit is becoming fairly routine. After 60 days, the process is about as automatic as it can become. That said, the study cited above found the average habit takes about 66 days to become automatic

The Talent Code

Instead, the teachers and coaches I met were quiet, even reserved. They were mostly older; many had been teaching thirty or forty years. They possessed the same sort of gaze: steady, deep, unblinking. They listened far more than they talked. They seemed allergic to giving pep talks or inspiring speeches; they spent most of their time offering small, targeted, highly specific adjustments. They had an extraordinary sensitivity to the person they were teaching, customizing each message to each student’s personality.

On John Wooden: Gallimore and Tharp recorded and coded 2,326 discrete acts of teaching. Of them, a mere 6.9 percent were compliments. Only 6.6 percent were expressions of displeasure. But 75 percent were pure information: what to do, how to do it, when to intensify an activity.


Learning Myths

  • Quizzing yourself on something you’ve just read is a great example of active learning, the best way to learn.
  • Research shows that deep subject matter expertise is a key element in helping teachers excel.
  • What is helpful is that [the feedback] comes close to when you perform the task, and that it requires you to generate an answer
  • Re-reading and highlighting are particularly ineffective. They’re just passive, and you are just kind of skimming that material.   If you’re preparing for a meeting, you’d be much better off just putting the material away and just asking yourself questions.
  • I think there’s so much stuff out there now that’s like, “Learning’s supposed to be easy, learning’s supposed to be fun!”
  • People underestimate how much they forget, and people who are able to revisit their learning at a regular rate end up learning a lot more.


My #1 Study Tip: The “Zone”

“Who dares to teach must never cease to learn”

Is this quote about the teacher possessing an unending fountain of knowledge to share, or that he must be able to relate to the nature of being a lifelong student?

Recently, I spent time relearning some higher level math. This material required focus, multiple passes, and drilling exercises to truly drive home the point and “own” the concept/knowledge (ie: be able to recognize it in the future and/or explain it to others). While requiring this 100% focus, I realized how many looming distractions I had at home which interrupt deep focus and thinking. The efficacy of superficial multi-tasking was debunked several years ago.  (More on that here, here, here).   It is one thing to get mindless work done while distracted (answering emails, etc), but it is a different matter entirely to learn something new and challenging with even minor distractions.

This made me reflect on my undergraduate studies in Mathematics and Computer Science, which routinely required deep focus and persistence.  In the early 1990s, dorms still resembled army style barracks with cinderblock walls and few amenities.  No TV, no cell phone, no texting, no landline phone (payphone at end of hallway), no laptop, no PC, no Web, no Facebook/Twitter (just a campus computer lab for typing papers). Despite such simplicity, it was *still* easy to get off-track in your dorm room (socializing friends, background noise, relaxing on the bed, listening to the stereo, etc) Therefore, we quickly learned that it wasn’t effective to study in your dorm room; it would take twice as long to do half the work.  Most students opted to do their serious work in the university library.  I took it a step further, and made a wooden “cubicle” in the isolated library basement my study place. Here, I could get into “deep zone” study for hours on end, with zero interference or stimuli to knock me out of the zone (See diagram below)

 A woman must have money and a room of her own if she is to write fiction.  -Virginia Woolfe

For certain types of work, sometimes the ideal environment is just quiet room with a desk.  As a high school teacher, I have told my students to find a quiet place at home to study free from distractions (siblings, TV, pets, Facebook, etc).  Today, I realize that I can’t stress this point enough.  I have noticed that some students now almost involuntarily check their cell phones without even realizing they are doing it.  While technology can be used as a learning tool, it can also open the door to interruptions and distractions.    This prevents them from entering (or staying in) the “flow/zone”.  A student must keep this in mind when establishing his ideal study environment in high school, college, and beyond.


Diagrams adapted from: Orientation to College Learning

Reliance on calculators can backfire

Math Skills Placement Test Practice

Here is a Math Placement test a student of mine was recently given by her prospective college.  Take a look at the questions, then notice the directions; they were not allowed to use any sort of calculator.  40 mins. / 40 questions.  This is a good example of where over-reliance on calculators for basic k-7 math can backfire.

Also, the AP Calculus exam has entire sections that do not allow the use of any type of calculator.

Study of Effectiveness of Various Learning Techniques

The 2 best rated techniques were:
Practice testing – Self-testing or taking practice tests on to-be-learned material.
Distributed practice – Implementing a schedule of practice that spreads out study activities over time, versus being massed in a short period of time

Low utility: Summarization, highlighting, the keyword mnemonic, imagery use for text learning, and rereading.
Moderate utility: elaborative interrogation, self-explanation, and interleaved practice.
Highly effective: Practice testing and distributed practice.

Explanation of the 10 study techniques

Improving Students’ Learning With Effective Learning Techniques

Before you hire a private math tutor…

Before you spend your hard earned money on a private tutor, first utilize the resources you are already paying for.  To that end, please encourage the student to help themselves.  (That’s what it’s all about, right?)  The lynchpin of my learning philosophy is to “teach a man to fish instead of giving a man a fish.”  Esoteric mathematical skills aside, use this opportunity to push beyond your comfort zone and improve your ability to learn anything.

  1. Print out my chart below
  2. Keep it in your notebook
  3. Try everything at least once.
  4. Hand it in to me

Please attempt every strategy at least once.  Print my chart, put it in your notebook, and check off each one after you do it once.  I think completing the grid within 2 weeks is reasonable.   (Sure, hide it from your friends so they don’t laugh at you.)  The goal here is to “nudge” and evolve your scholarship repertoire when reacting to a complex academic challenge.  Developing these habits will benefit the remainder of your academic career.


The Wrong Way to Prepare for the Math SAT

The Math SAT is an aggressively timed exam which hinges upon numeric, algebraic, and geometric foundations. The de facto approach taken by many SAT books, courses, and tutors focuses on doing sample SAT tests.  This is productive when the student’s SAT math foundations are already strong.  The student isn’t reviewing concepts at this stage, but rather, is practicing & optimizing. But, is this approach ideal for students who are just beginning to prepare for the exam?

I feel that effective preparation for the SAT entails a two stage approach. You should first back-fill core foundations before jumping into randomized SAT problems (which students may not yet be sufficiently prepared to tackle). In other words, targeted review “by topic” will prepare him for tackling the comprehensive practice tests. If you do 10 problems of a specific concept in a row, the concept is much more likely to “stick”. In contrast, prematurely doing practice tests can result in the following unproductive cycle: try a problem, get it wrong, move to an entirely different problem.

If you buy into my rationale, the key is to find an SAT book that clusters the practice problems “by topic”.

Excerpts from Rapt: Attention and the Focused Life

  • Learning tennis is best done between the ages of 8 and 15.  The longer you delay, the harder it will be, and your ability to play will suffer.  This principle applies to all sorts of skills, both physical and mental, including the ability to concentrate, direct your focus at will, manage your time.  Kids also need to work at developing the capacity for the concentrated, sustained attention required to succeed in many endeavors.
  • The young can get away with IM’ing while playing a computer game, but there’s a risk.  If you grow up assuming that you can pay attention to several things at once, you may not realize that the way you process such things is superficial at best.  When you’re finally forced to confront intellectually demanding situations in high school or college, you may find you’ve traded depth of knowledge for breadth, and stunted your capacity for serious thought.
  • Studies show that through practice, you can expand your capacity to focus.
  • Where big breakthroughs are concerned, getting to “That’s it!!” requires not only the intense focus and explicit learning …but also plenty of (non-conscious) incubation, mind wandering, and implicit learning.
  • Science has determined that multitasking, for most practical purposes, is a myth.  Focusing on 2 demanding activities simultaneously is a skill that requires months of drilling to acquire, and, even then, is confined to just those two tasks!
  • You may think you’re multitasking, but what you’re really doing is switching back and forth between two activities.  The extra effort involved actually makes you less productive.  Your overall performance will be inefficient, error prone, and more time consuming than if you had done one thing at a time.  If your train of thought is interrupted even for a second, you have to go back and say “Where was I?”  There are startup costs each time as you reload everything into memory, and people aren’t as good at is as they think they are.
  • When you focus on a demanding task, your brain’s hippocampus, which is important to memory, is in charge.  However, if you try to work while distracted by instant messaging, or the like, the Striatum, which is involved in rote activities takes over.  As a result, even if you get the job done, your recollection of it will be more fragmented, less adaptable, and harder to retrieve than it would be had you given it your undivided attention.


NYMag: Distraction

  • Poor retention:  “…when forced to multitask, the overloaded brain shifts its processing from the hippocampus (responsible for memory) to the striatum (responsible for rote tasks), making it hard to learn a task or even recall what you’ve been doing once you’re done.”
  • He sees our distraction as a full-blown epidemic—a cognitive plague that has the potential to wipe out an entire generation of focused and productive thought. He compares it, in fact, to smoking. “People aren’t aware what’s happening to their mental processes,” he says, “in the same way that people years ago couldn’t look into their lungs and see the residual deposits.”
  • If John Lennon had a BlackBerry, do you think he would have done everything he did with the Beatles in less than ten years?”

Procrastination and Setting Smaller Milestones

Here’s an interesting study that confirms what you already know about procrastination. You’re better off spacing out your work with self-imposed deadlines, if you want to avoid waiting until the last minute.  English teachers know this well, and that’s why they explicitly break up phases of a longer-term research paper into smaller, more regular milestones.

 They set up three classes, and each had three weeks to finish three papers. Class A had to turn in all three papers on the last day of class, Class B had to pick three different deadlines and stick to them, and Class C had to turn in one paper a week.

Which class had the better grades?

Class C, the one with three specific deadlines, did the best. Class B, which had to pick deadlines ahead of time but had complete freedom, did the second best, and the group whose only deadline was the last day, Class A, did the worst.



Q: When should I take the SAT II (Level IC)?
A: It can be taken after finishing Math 2 (Geometry)

  • Math 1: Algebra
  • Math 2: Geometry


Q: When should I take the SAT II (Level IIC)?
A: It can be taken after finishing Math 3 (Alg2/Trig)

  • Math 1: Algebra
  • Math 2: Geometry
  • Math 3: Selected Algebra2/Trig topics:
    • Imaginary numbers (i)
    • Systems of equations
    • Functions
    • Composition of functions
    • Logs
    • Trigonometry
    • Law of Sin & Law of Cos


Q: Are Math 3 (Algebra2/Trig) topics on the ACT?
A: Yes, about 8-10 problems out of 60.

  • Domain/Range
  • Systems of equations
  • Absolute Value Inequalities
  • Logs
  • Trigonometry
  • Radians (pi/180)
  • Sin/Cos graphs (0 to 2pi)

Computers at Home: Educational Hope vs. Teenage Reality



Computers at Home:  Educational Hope vs. Teenage Reality

The Duke paper reports that the negative effect on test scores was not universal, but was largely confined to lower-income households, in which, the authors hypothesized, parental supervision might be spottier, giving students greater opportunity to use the computer for entertainment unrelated to homework and reducing the amount of time spent studying.