Brain Aligned Strategy for Math Teachers! ( Using Stories!!)

Sometimes we need examples, especially in math of how you weave stories into secondary math courses… Below is one of the best examples to deepen learning and creating meaningful connections as this teacher weaves a story into ithe understanding of rational and irrational numbers! Story is at the end of the introduction!

Brain Based Teaching and Learning

Brain Aligned Teaching and Learning is a necessity to effective teaching and learning. Over the past 30 years, research has exploded with studies that demonstrate the power of teaching to the unique needs, intelligences, strengths, and aptitudes of all students. Educational Neuroscience intersects, is integrated and is a compatible foundational component for differentiated instruction, assessment, behavior management and an intricate aspect of a holistic education.

When we meet the child or adolescent where they understand “how” they process, retain, and retrieve information, we are creating a successful platform for deeper learning and an extravagant mastery of knowledge!

Author and educator Martha Kaufeldt states that neuroscience research may be in its infancy or specific to unique situations, but the new knowledge can provide teachers with insight into the behaviors, learning abilities, skill acquisition, and more importantly the emotional and social development of students. The research is confirming what great teachers know intuitively:

Students must feel safe and secure to maximize their ability to engage.
Novelty and joyfulness contribute to engagement.
Predictable patterns for behaviors and tasks can assist learners to know what to do next.
Multisensory experiences in enriched environments can enhance brain growth and development.
New concepts are acquired more quickly if they are hooked to prior learning and experiences.
If I had to sum up the dire importance of brain based teaching, in one sentence, it would be: Experience shapes and changes the brain! Teaching is the only profession where teachers have the great privilege to reshape the brain, because a child and adolescent’s environment and experiences literally affect the neural connections inside the brain directly impacting the emotional, social, and cognitive functioning of every student.

Learner –centered classrooms are brain compatible classrooms. Learner-centered classrooms are the seeds that grow, flourish and blossom when watered and cared for with the strategies igniting brain development such as incorporating choices, patterns, novelty, self-reflection, and physical movement inside academic instruction, assessment and assignments.

Emotions and cognition fit together like a hand and glove. When a child or adolescent is stressed or experiencing a perceived threat, the part of the brain responsible for executive functioning shuts down and learning is a moot point! When positive emotion is emitted, perspectives broaden and there, develops a relaxed alertness and focused attention that create clarity of thought! This is the optimal state of a mind for learning. Cognition and emotions are so intimately intertwined they directly influence each other. Making emotional connections drives attention and memory because when we are emotionally connected to subject matter, it becomes extremely meaningful and relevant.

There are four enemies of the brain that strongly inhibit the connections, processing and integration of prior and new knowledge. Threat, excessive stress, anxiety, and learned helplessness are states of mind that sometimes as teachers we activate unintentionally with frustrating results. Power struggles commence, hopelessness filters into the classroom and a sense of boredom and apathy loom inside the minds, hearts and instruction of many students.

Relational learning which is defined as: connections created between the heart and head of academic and emotional learning breeds higher test scores, motivated students and teachers, and escalating feelings of self-worth and self-efficacy. We cannot afford NOT to pay attention to the research and developments of brain based teaching and its positive results inside instruction.

Below is an example of a brain based strategy entitled story-chunking. This is a lesson that was developed by one of my graduate students, an inner city high school algebra teacher who has a student population that struggles with motivation and feeling successful with school in general. He developed this strategy to engage the interests, embedding creativity that every individual student embraces. When we engage the brain, we invite a variety of subject matter into the content areas we are teaching. This example below is an excellent portrait of a blend of language arts and math. We will discuss similar strategies during the presentation.

Story Chunking Rational and Irrational Numbers

On a crisp Saturday morning in late November, an unusually dense marine layer gradually blanketed the hillsides of Burbank, then Pasadena on its way towards conquering the skies of Los Angeles. As the invasion of aquatic fog continued its march inland, I stood beneath its imposing shadow of dullish gray. A swift and frigid draft swept across Baldwin Avenue and the sea of spectators packed on the sidewalk all braced their bodies in response to the sudden chill. Not a single muscle on my body moved as I looked towards the sidewalks, and saw the people in the crowd tighten their jackets and windbreakers. My thick uniform jacket and tight-fitting helmet sheltered me from the autumn gusts. To me, the draft felt like a gentle and comforting breeze as it splashed my face, washing away some of the tension and anxiety that had been building up for the last five minutes.

The fatigue of supporting the weight of my 30-pound tenor saxophone solely on my right arm began permeating my thoughts, but I disciplined my mind to ignore it as I continued standing at attention. In just four minutes from now, I will have completed the final performance of a parade I have trained every day after school for since school began in late August. I recall sweeping my peripherals with my eyes, and seeing my fellow band mates lined up in perfect rows and diagonals. The two hundred of us had woken up at 5:00 AM in the morning and boarded buses that transported us 115 miles from our school in San Diego to the quiet and tranquil L.A. suburb of Arcadia, where we annually compete in the most renown marching band festival in Southern California. Our school had won the championship every year for the last years. Adorned in our school colors as we fielded white jackets with neatly polished buttons, military hats with bleached feathery plumes, and royal blue plants with parallel white stripes streaking vertically down to our white marching shoes, we were poised to bring home the 6-foot tall trophy for a fifth consecutive year.

“Tweeeeeeett. Tweet, Tweet, Tweet!” After captivating the audience with his baton twirl, the drum major signaled to band that the stage was ours. The orchestrated cadence of drums and cymbals counted down the final seconds before our performance and then, on a syncopated off-beat, we played our first note of the march and a split second later, our band of 200 stepped off in unison to the low brass opening of “Washington Greys.” Two measures later, the woodwinds joined in, and then, the fanfare of trumpets cut through the air. Down the street we marched to the fast-tempo tune in the key of F-minor. I marveled at how impeccably straight and precise the rows, columns, and diagonals of our parade block remained as we glided down the street, perfectly harmonious in both sound and motion. Just two months earlier, my eyes frequently witnessed the vision of the exact opposite.

When the marching season began, our band was seemingly years away from the orderly and rationally cohesive performance ensemble we had shaped into by the end of November. Our first few practices were chaotic and confusing. Musicians who had not yet memorized the music kept playing off-beat, often influencing their entire instrument section to play in disagreement with the rest of the band. Our marching was greatly flawed, and I remember the ends of some rows would curve off by an entire yard from the center of the row. On extreme cases, we even had musicians bump into each other and trip then fall down when we were practicing our halftime field shows for football games. At times, the various horn sections of the band were playing 2 to 3 seconds apart from where the band was supposed to be during a song… Our band was a disorderly and chaotic mess on some days, unable to perform together rationally as part of a unified ensemble. Our band director held us to a high level of excellence, and had no tolerance for the disorganized display of confused and unorganized musicianship. So, he cracked down hard on us for the irrational mistakes we made, as he increased practice times and frequencies of practices. His hard and uncompromising approach towards subpar and irrational mistakes reminded me the Greek mathematicians Pythagoras and Hippasus.

Thousands of years ago, Pythagoras taught the brightest minds in Ancient Greece on the most advanced topics in math of that era. One of the mathematical ideas that Pythagoras advanced was the idea of rational numbers. Pythagoras believed that all numbers are rational, meaning that they can be written as a ratio of two integers. For example, the number 7.5 is a rational number, because it can expressed as a ratio of the numbers 15, and 2 if we write 15 and two as a fraction: = 7.5. Likewise, the number 2.33333333….., even though it is a repeating decimal is also a rational number because it can be written as the ratio of two integers. In the case of 2.333333, the two numbers are 7 and 3. If we place 7 on the numerator, and 3 on the denominator, then we come up with the fraction . Dividing 7 by 3, we end up with the answer: 2.3333333…..proving that 2.33333 is a rational number.

However, one of his students named Hippasus started creating disorder, and began disturbing the logical organization that all numbers can be expressed a ratio of two integers. Hippasus said that some numbers, like the square root of 2 (, cannot be expressed as a ratio of two integers. The value of is 1.414213562373095048801688724209698078569671875 37694 807317667973799…and so it continues without any pattern forever. When Hippasus tried to write the value of as a fraction of two integers, he found there is no solution. He could come close to the answer by solving for 99/70, but the answer was merely a close approximation, not an exact match. Other number values, such as the commonly used Pi, are also irrational… is equal to 3.14159265…and so the numbers continue without any pattern. Thus, Pi cannot be written as a ratio of one integer over another.

Pythagoras was deeply angered and disappointed in his student Hippasus. Just like my band director, Pythagoras would not tolerate a single student who operated out of alignment and in disagreement with the rest of the group. When Hippasus created disharmony within Pythagoras’ teaching by pursuing the idea of irrational numbers, Pythagoras realized that he could not tolerate Hippasus’ disorderly conduct. Since Pythagoras viewed the idea of an irrational number to be illogical and harmful towards his orderly organization of number theory, he knew that Hippasus could no longer be a member of his group. Pythagoras invited Hippasus out a on a sailing trip one afternoon, and threw Hippasus into the sea, drowning his student.

Although our band director was often mean and yelled at us for even the most minor errors in our musical performances, we knew that we were fortunate students because he would work with us on improving our techniques until we could perform as a rationally cohesive group rather than just drown us like Pythagoras did Hippasus when Hippasus discovered the existence of irrational numbers. After all, the ocean was just a few minutes away from our school…

Video link:

Math Lab Assignment

(Due Monday, September 20th)

This assignment is worth 20 points in the Labs/Projects category.

Write your own story, relating it to our lesson on rational and irrational numbers. In your story, you must:

1) Define what rational and irrational numbers are

2) State at least one example of a rational number and one of an irrational number

3) State the criteria for rational numbers.

Hint: Use your notes from class. Also, your story can be fictional. Your stories do not have to be tied to a life experience or a historical event like parts of mine are. In fact, I look forward to reading stories that are brilliant works of fiction.

Remember: You have complete creative licensing over this assignment. Your story can be set in outer space, the Triassic period, or a fictional universe. You can personify numbers into characters of your story if you’d like…maybe even create historical satire where one society is depicted as rational numbers, and another society as irrational numbers and explore the differences between the societies… or a league of rational numbered super heroes that is recruiting new members only if they meet the criteria for being a rational number… The possibilities are endless!

Be creative, and let your imagination take you to new places!!!

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