Tuesday, January 29, 2013

Mindset Influences Learning


Krakovsky, Marina (2007). The Effort Effect. Stanford Magazine, 25-32.

The key to ensuring that a student is successful is to tell them how smart they are, right?  Wrong.  In fact, telling a girl she is smart can actually hurt her ability to reach her potential.   Marina Krakovsky explores how mindset affects success in “The Effort Effect” published in the March/April 2007 edition of Stanford Magazine.  Her article is based largely on research conducted by Carol Dweck, a renowned scientist and professor at Stanford University, with regards to how people view intelligence.  Dweck’s research strongly indicates that students who view intelligence as fixed or inborn are less likely to succeed than students who believe you can improve and grow your intelligence. 

In addition, Krakovsky emphasizes that teachers and other adults are pivotal in how students view intelligence.  Numerous studies were conducted to show the different responses and achievements of students who had or were encouraged to have a native-intelligence mindset (you were born smart) or a growth mindset (you can grow intelligence with practice).  Students who naturally had a growth mindset or who were encouraged to think with a growth mindset were more likely to view problems and failures as opportunities to learn rather than as attacks on their individual worth and self-esteem.   They were also more likely to take risks, which are essential to expanding knowledge.  Students with a fixed mindset were more likely to prefer easy tasks where they felt competent and able to show that they were “smart” and live up to the adult’s expectations.  Below is a video of one such experiment directed by Dweck.



Looking at the effect of mindset is significant to the field of education, and especially relevant to teachers.  Children’s views of learning are heavily influenced by the primary people who teach them.  Teachers with a fixed mindset, or ones that encourage a fixed mindset, set students up for discouragement and a lack of ambition to tackle challenges.  These students will even lie about their scores to keep appearing “smart.”   This type of student values appearance rather than the acquisition of knowledge.   Teachers who encourage a growth mind set are able to help students reach their full potential by allowing them the gift of working through a tough problem without linking the outcome to their intelligence.  Students are much more likely to rise to a challenge when they don’t interpret a task’s difficulty with their own low ability. 

One of the most encouraging assertions in the article is that students can be taught to change their mindset to a growth mindset if they are given the opportunity.  The article references a very powerful study by Dweck and Lisa Sorich Blackwell of low-achieving seventh graders.  These students participated in one of two study skills classes.  One class taught students important study skills needed to succeed.  The other class taught these same study skills, but in addition, taught that the brain and memory operated like a muscle that grew stronger with mental exercise.  The students in the second class not only improved their grades, but their motivation as well.  The first group (the control group) showed no improvement despite the valuable study skills taught.  Krakovsky encourages “learning goals” rather than “performance goals” to emphasize the growth mindset.  Before educators think about what to teach students, it is a good idea to look at the students' mindsets first.

Krakovsky provides abundant studies to back up her premise that mindset affects success.  Her main source of information is the extensive research by Dweck in her book Mindset: The New Psychology of Success, written after 3 decades of research examining why some people reach their potential while others don’t.  With this background, Dweck and Blackwell used their research conclusions in the study of low-achieving seventh grade students to launch a new software for educators and students called Mindset Works.  Based on their findings, they invented a series of lessons to help students change their mindset and achieve their potential. 

Below is a link to Mindset Works.

Overall, the article has a powerful message to educators about the importance of mindset, and contains sufficient research to support the claims.  Students who are able or encouraged to see learning as a growth opportunity are more likely to succeed than students who believe intelligence is an innate ability.  Instead of praising children by telling them how smart they are, it is more beneficial to praise how much effort they put in.

Sunday, January 6, 2013

Divisibility Rule for 3 is Math not Magic

We all learn little "tricks" when it comes to math.  When I was in second grade, we learned subtraction by "borrowing" from one place over (not like we were going to give it back.)  Even with the better description of regrouping, many second graders are taught to memorize the "trick" for subtraction where you cross off and add a one to the tens place to the number on the right.    

While learning long division, 3rd graders at our local elementary school chant:  "Divide, Multiply, Subtract, Bring down"  and remember the steps by using (D- daddy, M-mommy, S-sister, B-brother.)  5th graders remember that to divide fractions, they flip the second fraction and multiply.  Unfortunately, all of this leads to students thinking that math is a bunch of tricks, that often don't make any sense. Students who memorize and compute well are "good" at math, when in reality, they are good at remembering patterns.  

I love to ask my students why they can do the "trick" to solve the math problem.  This makes some of them irritated (why are you making me do something other than the "math"), but some are curious.  These are the students who are budding mathematical thinkers, and are sometimes led to believe they aren't good at "math."

Here is a video explaining that in order to tell whether a number is divisible by 3, you can add the digits and divide the answer by three.  If it is without remainder, the whole number is divisible by 3.  Check it only if you are curious, because I would hate to irritate you!


Friday, January 4, 2013

Why Study that Algebra Stuff

In math classes across the country students are constantly asking when are they going to "ever use this stuff."   They use "stuff" like it is a bad word that actually leaves a sour taste in their mouths.  Sometimes teachers (including myself) give the answer that it is needed to function in the world.  However, for the basic life,  that usually applies to simple math such as cooking, check book balancing, and price comparison.  It is much more difficult to explain why students should find algebra useful.  In fact, I have often heard parents claim that they have never used algebra and cannot help their own students with this "stuff."

In reality, I think students are really asking why they should study algebra and not how they will use it.   Rarely do you ever hear art students question with dismay while learning to draw, "When will I use this stuff in real life?"   Math is the language of how the universe is constructed in pure form.  Not only does it explain many of the world's wonders, it also gives us a way to predict what might be before it is even discovered.  It can explain things we can't even see.  It connects all the disciplines and makes sense of our world. What student wouldn't want to be part of  that sweet and satisfying connection?  It is our job as teachers to not only make sure students can cook using fractions, but are also able to look at the beauty and connectedness of math to their world, and beyond.

I love this video where Samuel Khan takes a look at the beauty and connectedness of Algebra.


Thursday, January 3, 2013

Merry Christmath!

Merry Christmath!  Enjoy thinking of the 12 days of Christmas without the tedium of repetition and the benefit of lots of math.
http://www.youtube.com/watch?v=sxnX5_LbBDU