Math Pickle – students are left with raw and unresolved questions

MathPickle.com is a free online resource of original mathematical puzzles, games and unsolved problems for K-12 teachers. It is supported by the American Institute of Mathematics.

MathPickle.com is a practical resource for teachers. Its visually compelling puzzles and games engage students in tough problem solving. Its puzzles are organized by grade and subject – each designed for a 45-60 minute period. All have low-floor, high-ceiling. They engage struggling students in curricular skill acquisition, and deflect top students into tenacity-building challenges.

What does it teach?

MathPickle is not a curriculum. Instead, it showcases the gems of mathematics that are essential in every curriculum. Its activities span counting and patterns in kindergarten through to algebra, probability and Cartesian coordinates in high school. MathPickle goes beyond arithmetic and computation and gets students into a pickle. Lessons are not nicely wrapped up. Students are left with raw and unresolved questions.

How does it teach?

 MathPickle gives every student – especially the top students – a regular experience of failure – starting in Kindergarten. This removes the stigma of failure from the classroom. MathPickle also gives every student a regular experience of success. This requires that fast students are adroitly managed so as not to impinge on the full-hearted success of the methodical, slow problem solvers. It’s hard fun. We rejoice when students ask for “homework.” We laugh when they must be stopped from working and told to go outside for recess.

Unsolved Problems in Elementary School?

MathPickle’s long-term objective is to get unsolved problems in classrooms worldwide. The idea here is not to give students an unsolved problem and then laugh at them. A well chosen unsolved problem can be both curricular and can be presented in such a way to give vignettes of success. See some unsolved problems in classrooms here.

Only a fraction of unsolved problems are suitable for the school classroom, however there still are a huge number to choose from. The purpose of this conference was to gather mathematicians and educators together to select one unsolved problem for each grade K-12. Here is a pdf summarizing the winning unsolved problems. Here are the criteria used to make our decisions:

  • The problem is curricular. For example, Goldbach’s Conjecture (all even prime numbers more than two are the sum of two prime numbers) seems good for grade six students learning about prime and composite numbers, but it emphasizes addition too much for the grade six curriculum – hence Goldbach’s Conjecture should not be selected.
  • The problem is fun for the students. For example, the Gauss Lattice Point Problem (how many lattice points fit in a circle was curricular based for high school students working with conic sections, but failed to inspire many high-school students. However, the same problem worked better in grade three where the curriculum connection is area measurement.
  • The problem does not confuse students. For example, exploring Multiplicative Persistence is curricular based and fun for grade 4 students learning multiplication, but a few students subsequently became confused about normal multiplication rules – hence Multiplicative Persistence needed to be discarded or explained using a distinctive operator.
  • The problem is easy & cheap to implement by the teacher. For example, dice are common manipulatives in elementary schools, hence the use of dice in a grade five unsolved problem should be both easy & cheap.
  • The thirteen problems are as varied as possible. Some should be easy to explain on the radio, some should be games, some should be at the intersection of art and math, etc.
  • The problems should all hold stories – real or fictitious. The tragic life of Issai Schur might not be told in front of grade 2 classroom, but it can still inspire parents and teachers.
  • The creators of the problems are mostly white men. This needs to be rectified over time.
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