Students Present at Math Teachers Conference

Three Seventh Grade students traveled to Rye, New York to present a piece of creative, insightful work at the annual meeting of the Association of Mathematics Teachers of New York State (AMTNYS).  Angelina, Madison and Toti solved a challenging I Love Math problem last January when they were in Sixth Grade.  Here is the problem:

They struggled for a full week, and then came up with a highly creative and sophisticated way to explain their thinking and share it with an audience.  The puzzle they created has been shared with math teachers in national and regional workshops in San Francisco, Phoenix, and Morristown, NJ.  For the Rye conference, we invited to the students to present the puzzle themselves.

Here they are, explaining the challenge,

sharing their thought process,

and explaining the puzzle that captures the mathematical ideas in the problem.

Here they are celebrating after a successful workshop.  Their smiles tell the story:  they felt great about their talks.  Rightly so!

We are so happy that Angelina, Madison and Toti could share their work.  The truth is, many Mustard Seed School teams created remarkable submissions for this problem.   Any number of them could have presented their work.  The submissions were just that good.  In fact, several other student submissions were shared during this workshop.

In January we will launch another round of I Love Math problems.  Come back to this blog to see what what Mustard Seed's mathematicians are doing!  

Distinguished Mathematicians Visit Mustard Seed School

We are all mathematicians!  All of our students have been busy doing the things mathematicians do as they prepare for I Love Math Day.  Students this year have distinguished themselves by their persistence and their creativity.  There was broad-based success as students used all kinds of strategies to make progress on particularly difficult problems.  After finding solutions, they were extremely creative in finding ways to explain their thinking and their solutions.

On February 11, we will celebrate all of their excellent work.

Also, we will be joined by two guests who love math and who use it in their personal and professional lives.  They will be visiting students at every grade level.  They will share some of the ways they use mathematics.  They will hear about some of the problems students have been working on.  They will give math-related books and games to enrich our classrooms and libraries.  

One of our visitors will be Janine T. Cuervo, a Middle School math teacher at Trinity School, one of the most prestigious independent schools in New York City.  Our second guest is a computational chemist who does work for the pharmaceutical industry, Jennifer L. Knight, Ph.D.  She works as Associated Principal Scientist at Schrödinger, Inc. in New York.

If you see them at school on February 11, please welcome them!

Janine T. Cuervo:  Ms. Cuervo is a Middle School math teacher at Trinity School in New York City. Trinity was founded in 1709 by the historic Trinity Episcopal Church, at the corner of Wall Street and Broadway.  It is the oldest continuously operating school in New York City.  In 1895, it moved to its current Upper West Side location on 91st Street.  Ms. Cuervo teaches mathematics in grades 5 - 8.  She is has been the Math Olympiad Advisor since 2012.  She is interested in technology integration, including the use of SMART Boards, iPads, and interactive online resources in the classroom.  

Ms. Cuervo earned a Bachelor of Science in Elementary Education (2008) and a Master of Instruction (2011) from the University of Delaware.  She specialized in Middle School Mathematics and has Foreign Language Certification in Spanish.  She taught 6th Grade mathematics in Elkton, Maryland before moving to New York City in 2012.

Ms. Cuervo attended the November, 2015 conference of the National Council of Teachers of Mathematics in Nashville, TN.  She and a colleague from Trinity attended Mr. Lawrence's workshop on I Love Math Day as a way to build a culture of mathematics in a school setting, and at the same time help students grow as creative, persistent problem solvers.  These goals are aligned with hers, and we look forward to a robust collaboration between Ms. Cuervo and her colleagues at Trinity and Mustard Seed School on these topics.

Jennifer L. Knight, Ph.D.:  Dr. Knight is a computational chemist at Schrödinger, Inc. in New York City.  She and her team do computer-based research, and enjoy active collaborations with experimentalists.  Her focus is on developing methods for optimizing small molecule therapeutics and for exploring relationships between macromolecular structure and biological function.  This work is valuable to the pharmaceutical industry, by helping identify some of the most promising ways to develop new medicines and solve health challenges.  

Dr. Knight did her undergraduate work (Chemistry and Mathematics) and her M.Sc. (Chemistry) at Queen's University in Kingston, Ontario.  Her Ph.D. was completed at Rutgers.  She has done post-doctoral work at the University of Michigan and the Scripps Research Institute in La Jolla, CA.  She is a prodigious author of research articles and is the recipient of numerous academic awards and fellowships.  She teaches and mentors both undergraduate and graduate students, and is interested in helping women find pathways to success in math, science and engineering.

Dr. Knight notes that the company she works for, Schrödinger, is named after the physicist and his key equation developed in the 1930's that describes how molecules behave.  Dr. Knight's "lab" consists of desktops and large computer clusters (thousands of CPUs and GPUs) and the work is all about equations.  Dr. Knight's work is a good example of a dynamic we often discuss with Mustard Seed School students:  mathematicians can help us ask good questions.  Their equations and their thinking can help us imagine what ought to be, then go looking for it.  They can help us know what to look for, and where to look.  Two recent examples might be the recent discovery of the new 9th planet and the Higgs boson particle.  We look forward to learning from Dr. Knight how her mathematics can help find the next new development in pharmaceuticals.  

The Last Middle School Problem for 2016

February 11 is coming soon.  Middle School students are working on the final 2016 problem now.  The Canoe problem comes from a wonderful book called More Thought Provokers by Doug Rohrer, published by Key Curriculum Press in 1994:

The Penultimate I Love Math Problem for 2016

Last week, Middle School students worked on an intriguing problem as they continued to prepare for I Love Math Day 2016. This has quickly become one of my favorite problems.  Watching students struggle with the ideas relating to fractions, multiplication of fractions, infinite series and the visual representation of mathematical ideas has been fascinating.  Students were fully engaged with the rich content of this problem.

Give it a try:

How to Make a Third

Out of Fourths

Bob told his friend Mark that he could make the fraction 1/3 just by using fourths.  Mark did not believe him, so Bob showed him how:

(1/4) + (1/4)² + (1/4)³ + (1/4)⁴ + … = (1/3)   

Mark did not think this could be true, so Bob explained by saying, “Look at the picture below.”

“Ahhhh…..” Mark said.  “Now I get it.”

*     *     *     *     *     *     *     *     *     *     *     *     *     *     *     *     *    

You and your team need to do two things in your submission:

1.    Explain the meaning of the equation using words.  Come up with words that make the meaning of all those symbols clear.

2.   Figure out how the picture relates to the equation.  Come up with pictures, drawings or other explanations that would help a skeptic understand why the picture proved Bob’s point.

For students who had quick success with this problem, an additional challenge was

given:

How to Make a Third

Out of Fourths --

A New Challenge!

By now, you have become convinced that this equation is true:

(1/4) + (1/4)² + (1/4)³ + (1/4)⁴ + … = (1/3)   

You have seen how the triangle picture can be used to explain it.

Your challenge now is to come up with a different picture to demonstrate the truth of the equation.  Instead of a triangle, perhaps you could start with a square.  Can you think of ways to capture the ideas in the equation by starting with a square?

I Love Math Season Begins: The First Two Problems

I Love Math season has begun at Mustard Seed School.  Middle School students have already turned in their solutions to the first problem of 2016, and they are working on the second one.  Fourth and Fifth Graders will join the fun in about one more week.

The problem-solving we do in January sets the stage for the big celebration on I Love Math Day.  February 14, as everyone knows, is I Love Math Day. Since it falls on a Sunday this year, we will celebrate on the last school day beforehand, which is Thursday, February 11.  You will hear a great deal more about I Love Math Day as the day approaches.

Until then, there will be lots of creative problem-solving, as students struggle for a week at a time to prepare submissions for the judges.  They work in cooperative teams, so there is lots of practice talking about problems, developing alternative strategies, drawing pictures, organizing information, making mistakes, correcting mistakes, and coming up with creative ways to explain their thinking and their solutions.

So here is The Strawberry Ice Cream Problem

This is a rich and wonderful problem for middle school students.  It involves an array of math skills that students this age should be thinking about:  factoring, products, sums, uniqueness, proof, efficient counting, and organizing data.  It requires careful use of clues, that don't seem relevant, but are!  And the solution brings great satisfaction.

Over the course of one week, every middle school team found the solution!  Wonderful!

Right now, students are working on a very different challenge:  The Two Missiles Problem.  Parents are encouraged to discuss this problem with their children, and work together to solve it.  Enjoy!