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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…
Thomas Edison - "too stupid to learn anything"
Math is hard. Of course it can be fun and gratifying, but at times it can also be discouraging. Can a teacher teach students how to properly respond to failure?
Finding the right answer is sometimes not as important as learning to approach a problem correctly, having the willingness to study a mathematic question from different angles and resisting the urge to give up. This is best taught in middle school. In grades 6 – 8 if a student fails a test or gets a “D” or “F” in class, it has no effect on his or her college admission records. But this failure can become a valuable life lesson and, in fact, if approached properly a teacher can help students prepare themselves for high school, for college and even find good jobs. Here is what is needed: § 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…
Someone posted this on a Facebook page yesterday:
MATH TEST
2 + 2 x 2 + 2 x 2 – 2 x 2 =
a. 6
b. 16
c. 40
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…
Photography by Ta-Duc
When running for school board, one question was asked a number of times, especially in the debates and usually asked by students, “How will we provide more teacher/student interaction?” I assumed that students wanted a more personal experience in their learning until an article last week made me realize that a lot more was behind this question. The BBC News wrote, “Secondary school pupils are so scared of looking stupid in maths lessons they will not tell their teachers if they do not understand, suggests research.” The article continued, “The reasons pupils gave for not asking for help more often were that they were worried about looking foolish, were embarrassed or did not want to draw attention to themselves.” In other words, they lack confidence, which could be overcome if teachers had the time to spend more one-on-one with their students.
Are there other ways to build a student’s confidence in math? § 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 Damián 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…
This week we continue with the idea that we MUST engage our kids. Here is one of our favorite cartoons. Happy Valentine’s Day!
The cartoon introduces the Elevated Math algebra lesson entitled, “Solving Systems of Linear Equations by Substitution.” Graphing and elimination are both methods for solving, but substitution is another one. All three methods produce the same solution, but depending upon the problem, one method might be easier. Find this lesson in the iPad app, Elevated Math.
Photography by Thomas Favre-Bulle
An article in EdWeek this month by David Ginsburg entitled Don’t Prevent Students’ Mistakes, Prepare for Them has prompted this post. The article discusses how traditional teaching methods often deny students the chance to learn from their mistakes. But what about the teachers? Are they encouraged to make mistakes? Are they willing to take chances with their instruction? Is an unwillingness to create a video to use in a flipped classroom a bigger mistake than failing at the attempt?
In the traditional classroom model the information transfer takes place in class with assimilation of that information taking place outside the class. In an inverted model, as in a flipped classroom, the transfer takes place outside of class (often through online videos) and with assimilation in class. If implemented correctly, the class can become a robust environment where students work on challenging problems aimed at making sense of what they’ve seen and heard outside of class. Read our earlier blog if you need to know more.
I’ve spent the last couple months talking with teachers, visiting their classrooms, and reading blogs. I’m convinced schools should head in the direction of the inverted model and they should vigorously pursue the implementation of the flipped classroom.
A teacher I visited outside of Boston had a 6th grade flipped math classroom. It was a fascinating visit. Despite his struggles to keep § Read the rest of this entry…
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