Fraction Misconception

I am on a mission to help students master conceptual understanding of fractions. This is NOT an easy task. Fractions are so hard for kids whose minds still operate primarily in the concrete.

I’ve been tutoring some struggling mathematicians after school a couple days a week. This last week, we were looking at comparing fractions with different numerators and denominators. I showed the students region models that represented 2/3 and 3/4.

Just about every one of the 10 kids looked at the model and said that 2/3 was greater than 3/4. I was dumbfounded. How could the kids look at these two models, where one was clearly bigger than the other, and say the smaller one was larger?

I tried to get inside the heads of my students. Where was the misconception? Then it hit me. I had been showing numerous examples of unit fractions and pounding into the kids’ heads how 1/4 was smaller than 1/3, 1/10 smaller than 1/5, etc.

I did my best to drive home the point that the larger denominator actually indicated the smaller fraction. Then, we switched to comparing fractions like 3/4 and 2/3. Eureka! The kids were looking at the individual pieces, not the entire shaded region! When I asked which was bigger, they said 2/3 was greater than 3/4 because 1/3 is greater than 1/4!

Lesson learned. When kids seem illogical and out-of-touch, there’s a reason. Our job as educators is to pinpoint these misconceptions and help students make sense of the world around them.

For a really cool visual math resource, check out this fraction model on the NCTM website, Illuminations.

Have you discovered any math misconceptions with your students that you could share?

Human Alexa

 

 

 

 

An Amazon Echo is quite pricey. I accomplish pretty much the same thing in my classroom by playing the part of Alexa. Learn more about this technique as well as how to use an analog clock to teach angles in my latest episode of The 5-Minute MishMash podcast. Give it a listen and let me know what you think!

New Gallery Learning Website

I’ve been helping a ton of teachers get going on Gallery Learning, especially in North Country, New York. I recently created a new website where I will be sharing my ideas for Gallery Learning as well as those of other Gallery Learning masters. Check it out and let me know what you think!

Topics currently on the website: Building the Gallery, Glimpses from a Gallery Learning Classroom, training students to flourish in Gallery Learning, rules and procedures, subject matter ideas, lots of photos of student work, and more!

Official Gallery Learning Website

 

New Podcast from Tim: The 5-Minute Mishmash

It’s time for something new from the older and uglier Bedley Brother. I started a new podcast a couple of weeks ago. It’s basically a quick slam of teaching ideas. The show is about 5 minutes long with absolutely no fluff. I’m in my 29th year of teaching and have plenty to share. Each episode will feature such topics as technology, pedagogy, book recommendations, subject area tips, and a Twitter follow suggestion. I will only be recommending Tweeters with under 1,000 followers.

Listen to episodes 1 and 2:

I would greatly appreciate anyone who is willing to write a review on iTunes. Look for the show on iTunes beginning March 3 2017.

Do you like the new show? Let me know.

Develop Reading Fluency with Spaceteam App



Spaceteam app probably wasn’t created to help kids learn to decode rapidly, but it just might be the best method available. Spaceteam requires 2-4 players who all work on their Screen Shot 2014-12-25 at 9.40.45 PMown device to collaboratively solve meaningless problems. Each player is given a dashboard of gadgets with novel labels. Players see commands pop up on their screen. The only thing is each command is to be executed not by the player herself, but by one of the other Spaceteam members; therefore, the player who receives the command must quickly shout it out for another player to execute.

Screen Shot 2014-12-25 at 9.41.05 PM

The game requires speed, collaboration, multitasking, and most of all, quick reading skills. For students in grades 2 through 6, they play without even realizing they are working on reading skills, and that’s the beauty of it. The game is so engaging and fun, they will beg for more and more, and before you know it, will have fluency that is out of this world! Here are my own kids (mostly grown ups) playing:

Spaceteam is free with upgrades available for $4.99. It is currently available for both iOS and Android devices.

Book Recommendations for Teachers

 

The latest podcast upload from The Bedley Bros EdChat talk show features 2 impromptu guests that we pulled off of a Tweet call out at the last second. It was fun! The two educators who were willing to come on the show and play along with our silliness were Samantha Bates and Robert Hochberg. Here’s the booklist we compiled on the show:

Listen to the Podcast Here.

Developing Character in Our Kids



What makes a student successful? What makes adults successful? Is it how much they know? To me, it’s the character of a man or woman that makes the biggest difference. When I look back over my years of teaching, my biggest frustrations with students (and parents) revolve around issues like responsibility, dishonesty, short-sightedness, dependence, lack of perseverance, and lack of tenacity. As Angela Duckworth so eloquently details in her TED Talk, the biggest indicator of success is grit.

For years, educational “experts” have been telling us that students fail, students are mean, students are depressed because of their lack of self-esteem. I see students with the opposite problem: they are completely self-consumed and think of themselves as invincible. “I can drink and drive and will never get caught or get in an accident.” “I can be lazy and not do any hard work and turn out just fine. I’ll get by somehow.” Today’s young people suffer from a lack of character that revolves around an extreme self-centered attitude.

So if we want kids to focus more on others and develop strong character, what do we as educators do? Build up their SELF esteem? I believe that approach creates more self-centered, ego-inflated citizens. First, we can model other-centeredness, caring, giving, and kindness for our kids. We should be smothering them with positive messages, encouragement, and acts of kindness. In addition, teachers should be highlighting positive peer role models.

Friday, a 12-year old boy had a dream come true: he got a foul ball at a Red Sox game. But instead of standing up, celebrating his moment, and pocketing the ball, he turned to the little girl behind him and handed it to her. Ryan acted without even thinking! He did it because it’s nice to do! What an amazing role model. Let’s lift up Ryan and make him a hero for our kids to admire, rather than all the characterless actors, musicians, and athletes that our society loves to worship. And after you watch this, submit a comment with a link to other inspiring stories of selflessness that we teachers can use as positive role models for our kids.

The Bedley Bros Help Break Big Google News


Mike Lawrence, CEO of CUE, and Steve Hargadon, founder of Classroom 2.0, will be piloting a new Google for Education online training program for teachers. Listen in to learn more from these EdTech pioneers!

 

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