Thursday, August 28, 2014

Efficiency Does Not Always Follow a Recipe

Although answers are often set in stone in the math classroom, methods of deriving said answers can vary tremendously.  It is a common misconception that the best way to be a mathematician is to follow a uniform roadmap of steps.  In fact, giving students some flexibility in their approaches can make them grittier problem solvers.  Once multiples strategies have been shared, students can compare and critique using concrete examples.  It is critical that we allow students the opportunity to use The Standard for Mathematical Practice #3 and to debate in the math classroom.

Our first resource involves the image at the top of this post.  Students are often taught a set of steps when it comes to solving.  In this set of steps, distributing comes first.  Is this always the ‘best’ first step?  In the problem above, the student followed the traditional steps of solving and distributed first.  Wouldn’t it be more efficient to begin by multiplying both sides by the reciprocal?  Multiplying both sides by 4/3 would eliminate all messy fractions right off the bat and leave the student with a simple one step solving problem.  Different problems call for different approaches and efficiency does not always follow a recipe.  

If you haven’t already spent some time on the Open Middle website, I highly recommend that you do!  Thank you to Barbara Rappaport for reminding me just how powerful this site can be.  The notion is that every problem posted has an open middle.  That is, the beginning and end of the math problem are closed/fixed, but the middle is extremely open for interpretation.  The website includes hundreds of open middle problems organized by domain and ranging from Kindergarten to High School.

Finally, how do we assess argument in the math classroom?  I have created a rubric that specifically examines the Standard for Mathematical Practice #3: construct viable arguments and critique the reasoning of others.   Feel free to download and adapt the rubric from dropbox.

Thursday, August 21, 2014

How to Develop a Math Growth Mindset

Math ability, like IQ, should not be viewed as fixed.  I have blogged about this notion before in last November's post, Can Everyone Learn Math?  What is different about this week's post is the inclusion of resources to help students recognize themselves as capable math learners.

Why is it socially acceptable to say "I'm not a math person" or "I was never good at math growing up" when it's not socially acceptable to have the same reaction to reading?  In fact, I've never heard an adult say that they were not good at reading.  It would clearly carry different weight.  So how come we let our students, students' parents, and even co-workers claim to not be math people?  This is an issue that I come across almost every day.  Thank you to the 5 District Partnership Executive Administrator, Cove Davis, for sending me the article How to Turn Every Child Into a Math Person.

Many of you are familiar with Carol Dweck's book, Mindset.  But did you know that Dweck collaborated with computer scientists to develop resources that link video games, the growth mindset and mathematical learning together?  The proposed video games reward students for effort and perseverance when problem solving.  To learn more about this unique study, read Brain Points: A Growth Mindset Incentive Structure Boosts Persistence in an Educational Game.

Our final resource can and should be used in all math classrooms.  Jo Boaler, a professor at Stanford University, has introduced the Low Floor High Ceiling Tasks as a way to engage all levels of mathematicians.  If all students have an authentic entry point into a task, the activity is said to have a low floor.  If all students feel challenged with thought-provoking extensions, the task is said to have a high ceiling.  It is possible to create activities that offer both and give all students the ability to be mathematicians.

Wednesday, August 13, 2014

Girls Can Do Math Too!

For the first time in history, a woman has won the prestigious Fields Medal!  It was announced yesterday that Maryam Mirzakhani, a professor from Stanford University, has earned the 2014 International Medal for Outstanding Discoveries in Mathematics. Her research is absolutely fascinating and I encourage you to learn more about her work.  For details about Maryam and her proofs, please check out the following Stanford Report.

Ever heard of Danica McKellar?  No?  How about Winnie Cooper from the Wonder Years?  Now you can place her!  Danica happens to be an internationally recognized mathematician and advocate for math education.  She has written a book targeting young female mathematicians.  Take a look at Math Doesn't Suck for more information.

My final resource is not an article, a book or a famous mathematician.  It happens to be an engineering toy.  Goldie Blox is a construction toy designed for girls.  The picture above is the reason CEO, Debbie Sterling, created this product.  She decided it was time to develop and promote a toy that sparked the interest of young women.  She is committed to increasing the number of women engineers in our world and thinks that Goldie Blox can help with this incredibly important endeavor.

Tuesday, August 5, 2014

I, We, You vs. You, Y’all, We

Everybody I know who reads the New York Times felt the need to send me the article Why Do Americans Stink at Math? last week.  I reluctantly clicked on the link thinking it was going to be yet another political common core opinion piece either for or against the highly controversial standards.  I was pleasantly surprised with the article's refreshing message; it challenged our all-too-common approach in the math classroom of the "I, We, You" script.  Many successful countries ask their students to do most of their practicing outside of the classroom, while leaving the tough investigation for the precious time that the students get with their teachers.  So why do we spend so much time practicing in the United States? And what are some resources that we can use if we want to veer away from the traditional role of teacher as practice monitor? If you are curious about exploring the "You, Y'all, We" approach, take a look at some of these links below.

I can't say enough about Dan Meyer's Three-Act Math tasks. His inquiry-based approach lends itself perfectly to the "You, Y'all, We" script.  Act 1 serves as a hook where students watch an engaging video during which they formulate their own math specific questions. Act 2 requires students to work through at least one of their original questions by being provided with the important numbers and information. Finally, act three is where answers are revealed and discussed.

Teenagers across the country (and maybe even the world) have been playing the 'would you rather' game since the beginning of time. Now math teachers can leverage the power of this age-old game by using scenarios from the Would You Rather? Asking Students to Choose Their Path and Justify It website.

If you work with middle school math students, be sure to check out the PBS resource, Math at the Core: Middle School.  This website offers various videos and interactive tools that can be used to spark interest and excitement in the math classroom.  Incidentally, the advisor of this collection of resources is holding a webinar next Monday called Make Math Visual: Strategies and Resources for ELL Students. If you're interested in this webinar, register here