GREAT THINKING THURSDAY
For Klein ISD Educators of Gifted Learners
January 9, 2020
Bernshausen Elementary Teacher Inspired through Innovation
5th Grade Bilingual Teacher
Bernshausen Elementary
I am grateful to Klein ISD for organizing the Operation Lifeline Challenge! Several of our participants enjoyed the challenge so much that I encouraged and coached them to enter Jason Learning national Recycling Video and Poster Contest. They did months of research and came up with very creative ideas.
The Jason Learning 2020 Recycling Video and Poster Contest encouraged students to create a video or poster that imagined what recycling would look like in the future by designing a solution to current recycling problem now. The solution had to identify a current recycling problem, show how people tried to solve it in the past, and then imagine and design a new solution. For more information about the annual contest: https://www.jason.org/2020-recycling-contest
My Perspective
Innovation challenges are a great way to get students to apply their mathematical and scientific knowledge to solving real life problems. They also encourage teamwork, presentation/public speaking skills, and creativity. When we started on this journey, I never fathomed the solutions that the students would come up with: from edible water bottles to melting plastic bags. The students continued to show their perseverance and flexibility when their original idea and first few trials didn’t work out. As an educator, their dedication and creative spirits encouraged me so much as I watched them give so much effort to solving an environmental problem and making the world a better place.
Student Feedback
When asked, the only things that students wanted to change about the project was improving their own designs. The participants in every group wanted to continue to perfect their inventions and make a better product. Their favorite part of the innovation challenge was “creating something for the world” (Abraham Perez) and “feeling that I could change the world.” (Leila Flores). Of course, “using science” to create “mind blowing solutions to real world problems” (James Garcia and Leila Flores) and working with their parents to create solutions and videos (Charlie Elder) was pretty amazing too.
Driving Deeper Thinking through Questioning
By Christy Campbell, Klein Collins Site Coordinator and
Gordon See, Klein ISD AVID District Coordinator
Whether it is a class discussion over DNA or a Socratic Seminar over a current event, educators are always looking for ways to challenge their students to go deeper in their responses. In addition to the Revised Bloom’s Taxonomy, AVID trained teachers use Costa’s Levels of Thinking as a more succinct way to challenge students to take their learning to a new level.
Costa’s Levels of Thinking focuses on three levels. As the foundation, the students are challenged to gather their thinking (i.e. classify, recognize, explain). To build off of the foundation, the next level is to process their thinking (i.e. differentiate, interpret, deconstruct). To top off their linking, students apply the learning in some way (i.e. assemble, forecast, speculate).
Costa’s Levels of Questioning is an effective tool in teaching students to think more critically through higher inquiry levels. It identifies “levels” of growth and provides immediate support for them as they apply what they are learning to something new and challenging. AVID uses the house model that makes sense to the students, as it depicts a growth mindset in a more tangible form. They can recognize and willfully accept the path of intentional growth; soon, they discover great satisfaction in moving from one level (floor) to the next.
There are also opportunities to use Costa’s Level of Questioning during discussion opportunities like Socratic Seminar or collaborative study groups. By using the question stems, it gives students (and teachers) a place to start the discussion. The linked resource has question stems that are specific to the four core-content, but they can also be used in other subject areas as well! Students should be using question stems from all three levels to drive the thinking and the conversation.
In addition to driving learning and discussion, Costa’s Level of Thinking can be applied to note-taking strategies like LENSES and SOAPSTone. When using these note-taking methods, students work through different thinking applications thus going through the levels of Costa’s. Students should be encouraged to truly process the information they are asked to understand and challenge themselves to go deeper in their learning.
Teaching Costa’s Levels allows the teachers to witness more clearly the growth in their students, giving them first sight of those “Aha Moments” for which we all strive. When a student truly understands the three levels, he / she can apply it in ANY subject (including extracurricular ones) and experience true critical thinking. This growth mindset should be encouraged in every classroom. The result will be students who can enter the world with the ability to think independently, solve problems, and create growth in any situation. Costa’s Levels of Thinking is a tool for life.
For Inspiration and to Share with our Advanced Math Learners!
Advanced Geometry Students Publish New Integer Sequence
DG: In Fall 2019, our Advanced Geometry class officially published a new integer sequence in the Online Encyclopedia of Integer Sequences (OEIS).
DG: Please allow me to provide the background and context for why this is such an incredible achievement. The OEIS is the definitive record of integer sequences for mathematicians. An integer sequence is an ordered set of integers that counts something or many different things. The Fibonacci sequence is one that you may have heard of. Publishing a new sequence in the OEIS is considered an achievement for professional mathematicians and carries with it a mark of pride. Few undergraduates publish sequences, let alone middle and high school students, so this is quite a feat.
TGS: HOW DID THE DISCOVERY OF A NEW, UNPUBLISHED SEQUENCE COME ABOUT?
DG: We began the year by attempting to solve a problem about amoebas and blankets. The prompt was as follows: You have a pet amoeba that lives on a dot grid. Your amoeba always takes the form of a closed shape with boundaries along the grid, like so:
Your amoeba is cold and desperately needs a blanket, but it is very picky. It only likes perfectly square blankets whose corners all lie on dots of the grid on the boundary of the amoeba, like the orange square here:
Does there exist an amoeba for which no proper blanket can be found? This is actually an open question in the field of mathematics—mathematicians themselves don’t know the answer.
TGS: I ASSUME YOUR LESSON HAD AN EXPECTATION OF TEACHING THE STUDENTS HOW TO STAY RESILIENT THROUGH FAILURE — WHAT WAS THEIR PROCESS?
DG: Students began their collaborative problem-solving efforts with guess-and-check. They constructed amoebas and tried to find proper blankets for those amoebas. As a class, they quickly realized that guess-and-check is an inefficient solution method for this problem. It may eventually yield a solution, but it could take forever and is not guaranteed to find an amoeba with no blankets, even if one exists.
As they thought more deeply about the problem, the class came up with a brilliant idea: instead of creating amoebas and trying to find blankets that fit them, what if we enumerated all possible blankets and constructed an amoeba that “misses” at least one corner of every blanket. That would give us our desired blanket-less amoeba.
In trying to enumerate all possible squares, they discovered their integer sequence. The students realized that in order to count blankets, they had to specify the size of the dot grid. First, they let the grid be 3×3, then 4×4, 5×5, etc. At each size, they counted the number of squares. This list of total number of squares for each dot grid size is their sequence. The official link is here: A328152 (“328152” is the catalogue number of their sequence within the OEIS). We submitted the sequence on October 5, and it was published October 21, 2019.
TGS: IT MUST BE VERY FULFILLING AS A TEACHER TO SEE YOUR STUDENTS ACHIEVE THIS HONOR.
DG: It’s fantastic. I am incredibly proud of their collaborative problem-solving approach that enabled them to find and publish new mathematics.
For more information about Derek Graves, please visit Inspiring a Mathematical Playground in the Classroom.
Source:
Bellis, N. D. (2019, December 31). Students Publish New Integer Sequence: The Grayson School. Retrieved from https://thegraysonschool.org/advanced-geometry-publishes-new-integer-sequence/.