I recently came across an old Wall Street Journal I had not thrown away. The headline said, “Wandering Mind Heads Straight Toward Insight,” and the sub headline reads, “Researchers Map the Anatomy of the Brain’s Breakthrough Moments and Reveal the Payoff of Daydreaming.”
Here’s the question we each need to ask ourselves: Are we giving ourselves enough time to daydream?
One of my students wrote me recently that “getting a good idea is like catching a fly.” A good analogy. I’ve caught flies out of the air, and it requires both concentration AND the ability to relax and go with your intuition. Consider one of the examples in the article. Rene Descartes who, while lying in bed watching flies, realized that he could describe a fly’s position by coordinate geometry. The point is, getting a good idea requires putting the problem in front of you and then letting your mind wander.
The article says, “our brain may be most actively engaged when our mind is wandering and we’ve actually lost track of our thoughts…” One researcher suspects that, “the flypaper of an unfocused mind may trap new ideas and unexpected associations more effectively than methodical reasoning.”
Insight favors a prepared mind, which means that we still need to sit down and attempt to work out the solutions. But then, after we have looked at all the different options (writing them down helps tremendously) we should forget about the problem for a while and let our minds wander.
If we want our S.T.E.M. programs in our schools (or homes) to succeed, we need to encourage our students to approach problems insightfully – with discipline, but also the time to nurture the question, to let it swirl around in thought and to daydream about it a little. Then our students will catch lots of flies. (sorry, can’t let go of the fly analogy!)
Oh, one more thing, researchers have found that “People in a positive mood are more likely to experience an insight. How you are thinking beforehand is going to affect what you do with the problems you get.”
With over 650,000 apps in the App Store, how do you determine what’s really worth your time, and in some cases, money? As a middle school math teacher and summer math enrichment program director, I’m always looking for new games and ways to engage my students. I have spent countless hours scouring the App Store, downloading and testing out various apps, sometimes even getting addicted to some myself! Without further ado, here is my list of the five best math apps currently on the market. § Read the rest of this entry…
Pages from Da Vinci's notebook - Photography by Maia C
Last week a principal introduced me to a math teacher in my school district. The principal proudly stated that over the past three years this teacher’s students had averaged 98% advanced or proficiency in Algebra 1.
“Wow! How did you do that?” I exclaimed. “Is there something special in your teaching technique?” Obviously, this teacher knew her subject, but so do many teachers and without achieving these results.
“I care for my students,” she responded.
Okay. Yes, caring does have a lot to do with a teacher’s success. We wrote a blog about it in February called We MUST Engage Our Kids. Caring was one of four ways that we suggested. But 98% advanced? Can “caring” account for that kind of success? After I pressed for more information, this teacher finally revealed § Read the rest of this entry…
Two months ago we posted an article entitled: We MUST Engage Our Kids. Here we listed what we considered the necessary ingredients for a teacher to conduct a successful math class. These were passion, real-world problems, humor, and caring. The other day I was chatting with Vijay, a math tutor working in Romania, and he sent me a short article he had written about how he had started tutoring. I found it fascinating. Two of the ingredients really stood out (though I’m sure he uses all four). Can you guess which two? Here is his article.
It all started about two and a half years ago when I was told to leave Oracle where I was working in Bucharest as an educational consultant. § Read the rest of this entry…
We discovered an article posted five years ago and thought it worthwhile to share. The article reveals ten easy arithmetic tricks.
We know many teachers do not like parents teaching their kids tricks, but once students have demonstrated conceptual understanding, learning tricks makes math so much more fun. § Read the rest of this entry…
And I was shocked to see that so many people got the wrong answer.
Knowing the Order of Operations is important for a student’s success in math – so important that we included two lessons in the Elevated Math iPad app dealing exclusively with this subject.
If you are absolutely sure of the right answer, don’t bother watching the following videos. BUT if not… or if you want a peek at how Elevated Math teaches the Order of Operations, § Read the rest of this entry…
Math students who begin their journey into absolute value usually evaluate expressions with absolute value as “always positive.” That is until they encounter the absolute value of zero, and then their answers become “always positive or zero.”
The formal definition of absolute value is |x| = x if x ≥ 0 or –x if x < 0. The negative x confuses students, and they never quite understand that it is the absolute value that is always positive or zero. Unless this misunderstanding is corrected, the situation becomes more problematic when solving inequalities that involve absolute value, which can lead to unhappy teachers and muddled students who usually conclude, “we don’t like math.”
In our Elevated Math lessons we make it clear that absolute value is distance, and distance is always positive or zero. We begin in lesson M3.1 with instruction on negative numbers followed by problems, and then we introduce the concept of opposite numbers before explaining absolute value:
A short article written in a 2006 issue of NCTM’s mathematics journal, Teaching in the Middle School, caught my eye. It was entitled “Some Students Do Not Like Mathematics”. The reasons stated were the same as we have heard for years: “We don’t engage our students,” “Parents are not involved,” “Students don’t know how to expand their thinking when they solve a problem.”
I object to hearing a problem discussed without including at least one concrete solution, and this got me thinking: What solution(s) would I offer if I had written this article.
Of course, my first advice would be to buy an iPad and download the Elevated Math lessons. Most students enjoy math when they watch the videos and work the problems.
A memory of middle and high school is being stuck in class and daydreaming my time away, full aware that my inability to focus on the droning lesson in front of me would cost me dearly when I had to figure out later how to answer the homework problems. Maybe this is why I made educational films in college and more recently worked with a team to launch Elevated Math, an iPad app that teaches middle school math. Teachers need to do something to engage our kids. We have infinite ways to do this, but for now I’ll touch on four.
1. Passion. Teachers must not only love the subjects they teach, they must be passionate about them. In college, I took a class on existentialism. The instructor would talk an hour in the lecture hall and then, when the hour was over, would invite us to join him in the sculpture garden outside where he would lecture another hour. Everyone followed him. He would speak about each philosopher as if this person held the ultimate truth of life that we each needed to know. No doubt this professor passionately loved his subject. Can we approach our class in the same way, as if we hold a sacred gift of knowledge that we must pass on?
2. Real-world problems. I remember my earth science class when the first photographs of the moon were released. My teacher drove to Washington D.C. (we lived in northern Virginia) and acquired large prints of these maps. § Read the rest of this entry…
If you have taught your math students about perimeter and area, if you are ready to present them with an application challenge, and if they are into Pythonesque comedy (Do you know many middle schoolers who are not into the absurd?), consider showing this clip from Monty Python and the Holy Grail.