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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…
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…
Someone posted this on a Facebook page yesterday:
2 + 2 x 2 + 2 x 2 – 2 x 2 =
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:
Here is how we do it: § Read the rest of this entry…
Illustration by DamiÃ¡n Navas
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.
But that’s an obvious answer. What else could I say? § Read the rest of this entry…
2011 will forever be significant in Elevated Math history. Our iPad app was launched along our website and blog. In Barbara Walters’ fashion, we decided to list the TEN MOST FASCINATING POSTS in 2011. Oh, ok. Fascinating is probably not the most accurate adjective, so how about if we list our ten favorites?
- Angry Birds Can Teach Math was one of our most popular posts. It showed how to teach parabolas and quadratic equations with the Angry Bird game. We followed this up with Use Angry Birds to Teach Math Pt 2, which includes a portion of the Elevated Math lesson.
- A Case for the Flipped Classroom is a subjective examination of one the hottest ideas for teaching math that came out this year.
- Making Math Relevant May Be the Key was also one of our most popular posts. It details how a teacher made math relevant to a class of potential drop-outs. § Read the rest of this entry…
Variations of flipped classrooms are as many as there are teachers. Brian Bennett writes in his blog post, “The flipped class is an ideology, not a methodology.” He stresses that it is not defined by the use of videos. He has moved away from videos now that he has more time for “engaging activities and labs.” The flipped classroom is all about “making connections with learners and differentiating your instruction.” Therefore, a teacher can have such a classroom as long as the needs of all learners are being met. Bennett is commended for meeting the needs of his learners. However, for a classroom to truly be “flipped,” prepared instruction must continue at home, not just in the classroom.
The way we like to understand the term, the flipped classroom is used to introduce and reinforce the teaching in BOTH the classroom and at home. For example, a teacher introduces and provides direct § Read the rest of this entry…
- Photography by Jon Hayes
I’ve been doing a lot of reading this summer, and I’ve come across a few books in the past few months that I think every math educator should read.
“I don’t see how it’s doing society any good to have its members walking around with vague memories of algebraic formulas and geometric diagrams, and clear memories of hating them.” ~ Paul Lockhart, p33
The original essay that inspired this book is still available online here, and if you can’t find the time to read all of Paul’s book, I recommend at least reading the essay. Paul talks passionately about some serious problems in mathematics education today, most notably that much of what is taught in schools is not actually mathematics itself, but a caricature of mathematics.
Mathematics Miseducation by Derek Stolp
“[M]athematics, as it is taught, does not give children any view of reality, let alone a rational one.” ~ Derek Stolp, p33
Derek argues first that mathematics, as it is taught today, does not warrant inclusion in our curriculum, but then demonstrates some clear ways that mathematics education could be changed to make it viable again. He has the best argument for a constructivist approach to mathematics education I’ve read so far. § Read the rest of this entry…
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