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…
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.
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…
On May 23, 2010 in my very first blog, Teaching Math; It’s All in the Balance, I shared my view that both the traditional and reform camps have something to offer math educators. Basically, traditionalists believe skills should be taught based on algorithms, formulas and step-by-step procedures; reformists support a more inquiry-based approach that emphasizes developing conceptual understanding and problem-solving skills. My contention is that a balanced approach is best. Also, I am an advocate for using engaging, interactive technology whenever possible to reach and teach this generation.
I shared a conversation I had with Grant, my oldest grandson, about adding two two-digit numbers. During our talk it was obvious his skill for adding single digits was developing nicely, but he lacked an understanding of place value concepts. Even though he could get the right answers, when I asked him the value of the digits, he had no clue.
In my second blog posted on June 27,The First Steps in Developing Conceptual Understanding of Place Value, I emphasized the importance of developing a foundation of understanding. I also shared ways to help children understand place value when first learning to count with non-proportional items (straws and money) and with proportional manipulatives (base-ten blocks) when adding and subtracting.
Grant is now in the 3rd grade. He tells me he “gets” math. He doesn’t need my help, thank you very much. That is… until this week. Monday, he called to say he had taken a test last week, and he wasn’t happy with his grade. “Can I come down, Gigi? Can you help me?” Smile. Gigi is back in the picture.
In the previous blog Use Angry Birds to Teach Math (see below) we shared a plan to introduce students to parabolas. Students can follow Bruner’s CRA teaching method from tossed-beanbags to the parabolas in Angry Birds to graphing-quadratic-equations in Elevated Math. The popularity of our blog post has inspired us to include an excerpt from the Elevated Math lesson. This lesson is part representative and part abstract. We have removed from the video the “autopauses” found in the iPad lessons so the video will flow better. This lesson, A14.1, continues for another 18 minutes and includes abstract activities for the students. Also, two subsequent lessons A14.2 and A14.3 further explore quadratic equations.
As David Wees shares in his blog entitled, Make Mathematics Fun, “too many students spend a lot of time not enjoying themselves when learning mathematics.” He challenges mathematics educators to make math accessible and more easily learned for their students. Being up for the challenge, here is a suggestion.
Angry Birds is the largest mobile app success the world has seen so far. It is an interactive, animated projectile launcher that creates parabolic motion. The parabola is traced by the flight of the projectile (the bird). In the app players use a slingshot to launch birds at pigs stationed on or within various structures. The goal is to destroy all the pigs on the screen. The game is such a huge hit that The MIT Entrepreneurship Review predicts that the game will be bigger than either Mickey Mouse or Mario. If kids are that into it, let’s change it from a mindless game to a vehicle for learning math.
On August 18, 2011 a panel of experts discussed the state of black education in the U.S. at the Edgartown Whaling Church, in Edgartown, MA. The topic of the evening was Separate But Unequal: Closing the Education Gap. The online publication, the Vineyard Gazette, ran an article written by Mike Seccombe summarizing the discussion entitled Poverty and Failure of Education System Weigh on Black Students. I learned about it from Diane Ravich’s tweet. § Read the rest of this entry…