May 2018
Curriculum, Assessment, and Instruction Dr. Fatima Morrell, Assistant Superintendent Our Vision: Through a commitment to equity and excellence, all students will receive a rigorous instructional program which prepares them to compete successfully, and contribute responsibly in a global society.
Assistant Superintendent Highlights
“Mathematics is Everywhere”
Take a look around and math is everywhere. From finding the best deal while online shopping to calculating our students’ grades to cooking tonight’s dinner. When we think about math we tend to think about numbers and operations, fractions and decimals, standard algorithms and complicated formulas. But when was the last time you stopped to think about the stories behind the math? The who, the what, the where, the when? Stories connect us. They help us to create a deeper understanding and discover where we fit into the big picture.
Have your students ever asked, or maybe you, yourself have wondered, “Why does this matter? When am I ever going to use this?” It’s these questions that show us how critical it is for students to understand both the history of math and the future of math.
There are so many people that label the way students today are learning math as the “new way of doing math.” But how “new” is this math? The Ishango bone from Ancient Africa is one of the earliest artifacts of arithmetic, dating back 20,000 years ago. Many similarities can be found when comparing our base-10 number system to the base-20 number system Ancient Mayans used. Using shells to represent zero, dots to represent ones, and sticks to represent a groups of five, Mayans were able to calculate mathematical problems such as the length of the solar year. The importance of astronomy and calendar calculations in Mayan and Mesoamerican society required May 2018 mathematics, and the Maya constructed quite early a very sophisticated number system, possibly more advanced than any other in the world at the time, which speaks to their mathematical genius ( http://www.storyofmathematics.com/mayan.html ). Many students from our Latino cultures may find these mathematical concepts and facts quite interesting as they will be able to make historical and cultural connections to ancient Mayan and Mesoamerican mathematicians to whom many can trace their cultural roots.
Ancient Ethiopians developed a system for making computations that focused on halving and doubling numbers. This base-2 number system is very similar to how computers function today. Bringing some of this information into the classroom is a fun and interesting way for students to find similarities and differences with the math they are studying right now. Many students are also able to make historical connections with Ancient African and Mayan mathematicians. Take Imhotep for example, a Black man who was the architect of the Step Pyramid at Saqqara, and whom many scholars consider a multi-genius on the subjects of math, science, medicine and other scholarly areas. Many students will be able to make a cultural connection to such a genius who may share their ancestral background.
What do we know about other Native American uses of early mathematics? According to significant research(study.com) Native American societies used either base-ten or base-20 counting systems, and recorded numerical data through notches in wood, woven chords, and painted bark, among other lightweight and transportable systems. Some even used their fingers. By using different combinations of fingers and a complex understanding of multiplication, some Native American cultures could count up to 1,000 using their ten fingers alone! I am sure our Native American learners as well as all learners will find a study of this early mathematics phenomenon quite interesting, and therefore engaging.
A history of math that includes facts from all around the world, helps our students to see themselves in the curriculum and find where they fit in. Making these connections help students to build confidence related to the curriculum content, while gaining an understanding of how and why mathematical content is relevant in their everyday lives. Seeing the connections between math and computer technology, engineering, astrology, and the medical fields will provide our students answers to the common questions: “Why does this matter? When am I ever going to use this?”
Knowing that the math of today has been developed over years and years of hard work will hopefully foster a growth mindset in our students. They can do this! And it is our job as educators to promote a positive math culture in our classroom. The next time your students question the importance of math, try adding some math history to your lessons.
In this May edition of the CAI newsletter, each department discusses important mathematical curriculum content connections to their specific subject areas and make suggestions for strategies and best practices that can be used to develop cross-curricular alignment and understandings during classroom instruction. We hope you will find this useful to your instructional practice.
Thank you, Dr. Morrell (with contributions from Nicole Buccilli) May 2018
Important
Dates
May 1-3 3-8 NYSED Math Testing
May 7-8 NYS Math 3-8 Scoring Training Building Level Lead Teachers (8:15-3:30@BPDTC) J. Wagstaff
May 8 English Language Arts Instructional Updates Teacher Appreciation Day
May 9 This year has been named “The Year of Instruction.” Early Release Day After many classroom visits, our Chief Academic Officer, Anne Botticelli developed the instructional priorities for May 10 classrooms in grades 3 through 12. Principals, assistant Superintendent’s Conference Day principals, and coaches were presented with the priorities May 11 during monthly meetings and charged with bringing the NYS Math Grade 7&8 Assessment Scoring priorities to teachers. Detailed below are the BPS (8:15- 3:30@BPDTC) Instructional Priorities and additional information as it was J. Wagstaff presented to district personnel: May 14 Pre-K Art Show BPS Instructional Priorities for ELA: City Hall @11:00am
Instructional & Math 1. DISTRICT MATERIALS: Are District materials and Coaches Meeting curriculum being used effectively and with skilled fidelity? (8:15-3:30@#187) J. Wagstaff Students consistently use and/or respond to District-vetted materials, including texts, assignments and questions. May 15 Teachers follow District curriculum as intended (e.g. on Trauma Informed Care Gr. K-3 (8:15-3:30@BPDTC) track with District pacing and instructional guides from the N. Bycina District website; using rigorous questions, tasks, and assignments provided by District-vetted materials.) May 16 Balancing Language and Literacy – Module and/or lesson numbers from the materials are clearly Bilingual Teachers posted in the classroom each day. (8:15-3:30 @BPDTC) 2. ALL STUDENTS READ: Are all students reading anchor May 17 texts independently on a regular basis? Richmond Speaking Contest Students engage in daily accountable, independent reading (10:00@Roswell Park Hohn Auditorium) of grade-appropriate anchor texts and/or decodables. J. Romain May 2018
Teachers chunk readings and appropriately assign accountable tasks (e.g., annotations, prompts, summaries) May 18 Literacy Coaches Meeting as students read anchor texts silently. (8:15-3:30@BPDTC) J. Byrnes Students in grades 3-12 spend the majority of class reading, writing about, and discussing grade- and May 21 Grade 7 & 8 Mathematics League subject-appropriate texts. Awards Banquet 3. ALL STUDENTS WRITE: Are all students writing to Emerson @ 10:30am demonstrate deep understanding of the anchor text on a J. Wagstaff regular basis?
Students have frequent opportunities to write independently May 23 in response to what they have read, allowing them to Social Studies PD with NYS demonstrate their independent understanding of the text. Education Department Students consistently respond to text-based questions, Buffalo History Museum 4:30-7:30 using evidence from the text to demonstrate their Social Studies CLTs understanding. Students respond to higher order thinking questions (HOT!) that target the depth of grade-level standards. May 22-25 June Earth Science Regents Administration of Part D 4.DIFFERENTIATION: Do all students have the support they K. Baudo need to access grade-level content? May 23-25 Grade 4 & 8 State Science Test - One of the most important concepts behind differentiation is Performance Test Administration that students are working productively on skills that they K. Baudo need reinforced. When teachers use vetted resources, we know that the time is well spent. May 28 Memorial Day The teacher deliberately checks for understanding Schools Closed throughout the lesson and adapts the lesson according to May 29-31 student understanding. June Earth Science Regents The teacher scaffolds instruction and tasks for various Administration of Part D (34) K Baudo students allowing students to access grade-level content * and demonstrate independent understanding without Grade 4 & 8 State Science Test - reducing the rigor of the standards. Performance Test Administration (120) K Baudo The teacher pre-teaches, re-teaches important skills and concepts through teacher-led small group instruction. The teacher differentiates activities for use in groups or in learning areas to provide targeted practice of previously taught skills/concepts.
May 2018 Culturally & Linguistically Responsive Teaching by CLRT Committee (Kelly Baudo,Chair; Michele Agosto; Crystal Benton; Dalphne Bell; Michael Cambria; James Schwanz)
In the Culturally and Linguistically Responsive Teaching programs we emphasize knowing oneself and one's ancestry. It is essential for students to be able to relate to and see themselves in the information they are learning. As we look at the world of math, we can see it's all around us. Skills we learn in math are transferable to our daily activities and are the foundations of most decision we make. When one thinks of mathematicians the first names that may pop into your head are most likely Sir Isaac Newton Sr. or the great mathematician and physicist Albert Einstein. Unfortunately, through restorative circle discussions and cultural lessons, it has become apparent many students cannot name mathematicians that look like them or the contributions they’ve made to our culture and society. At times failing to connect to the content of the math lesson causes a decrease in interest among the learners. Dr. Christopher Emdin in his book “ For White Folks Who Teach in the Hood and the Rest of Y'all Too,” stated educators must step out of their comfort zone. This means educators must not only learn about their students' backgrounds but understand and value them. This action will provide you with an opportunity to better engage with your students during the lesson. Teaching the most challenging mathematics lesson can be less challenging if presented in the context your students can relate to or find useful. Once students feel a sense of belonging in your classroom, the use of the material in the lesson, and influence of the teaching in their lives and community, they will be more inclined or interested in the perspectives, facts, and concepts you are presenting. As you continue your process of connecting content to the interest of your students, please share the mathematicians below we shared during the Our Story Program and My Brother’s Keeper All Male Academy.
Imhotep was an Egyptian polymath (a person expert in many areas of learning) best known as the architect of Step Pyramid at Saqqara. Imhotep was a priest, advisor to King Djoser, a poet, physician, mathematician, astronomer, and architect. May 2018
Mathematics was vital to astronomy, calendar calculations, and sophisticated number system of the Mayan society.
The Ishango Bone is approximately 22,000 years old, making it the oldest evidence of mathematical practice in human history. The Ishango Bone was found in a village between Uganda and Congo.
Benjamin Banneker was a largely self-educated mathematician, astronomer, compiler of almanacs and writer.
Elbert Frank Cox an American mathematician who became the first black person in the world to receive a Ph.D. in mathematics.
Euphemia Lofton Haynes the first African-American woman to earn a Ph.D. in mathematics. May 2018
Víctor Neumann-Lara a Mexican mathematician, a pioneer in the field of graph theory in Mexico. His work also covers general topology, game theory, and combinatorics.
Julio Cesar de Mello e Souza a Brazilian writer and mathematics professor. He is well known for his books on recreational mathematics, published under the pen names of Malba Tahan and Breno de Alencar Bianco.
Katherine Coleman Goble Johnson an African-American mathematician whose calculations of orbital mechanics as a NASA employee were critical to the success of the first and subsequent U.S. manned space flights.
May 2018
Early Childhood and Math Department by: JaDawn Wagstaff, Director and Dalphne Bell, Elementary Ed. Department Supervisor By: Jessica Sipes, Supervisor and Nicole Bailey, Project Administrator I present you with this challenge…
”list the things that you do each day that involve math The Building Blocks of Math Comprehension and/or numbers in some way….and leave those things out of your life for just one day. Of course, this Throughout the district in Pre-Kindergarten means you’ll just be in bed all day because your classrooms, Building Blocks math program is utilized alarm clock has numbers!” each day. Doug H. Clements and Julie Sarama, from the University at Buffalo, created this curriculum What does this day without math/numbers look like? specifically designed for Pre-K. The program is It means... developmentally appropriate and integrates the five ● no clock, thus no time strands of mathematical proficiency: Understanding, ● no calendar, thus no date and no birthdays Computing, Applying, Reasoning, and Engaging. ● no currency, thus no cash, no bank accounts, and At its inception, Building Blocks was the first of its no shopping kind. Where the focus of most math programs was ● no measurements, thus no recipes, no buildings, teaching students a process of steps to gain a no houses, no schools, and no hospitals solution, Building Blocks focused on the concept ● no technology, thus no computers, no televisions, no cell phones, no cars and no electricity development with the main goal being for students ...just to name a few challenges! to have a true understanding. This program incorporates both technology and purposeful use of Since we know that students will ask, “when will I manipulatives into each lesson. Daily lessons are broken down into four parts: Whole Group, Work ever use this”, make a concerted effort to have an Time, Reflect, and Assess. In whole group teachers answer ready. The more that answer has begin with a warm-up, which reviews a previously implications,or ties to, the things they deem most taught skill followed by the new skill they are important, the more we emphasize the importance of developing. Work Time is broken down into mathematics in our lives, and for our livelihoods. teacher/teacher assistant led small groups, a computer center, and a hands on math center. This program uses data gathered from informal assessments to determine each student’s individual progress on multiple mathematical trajectories. Melissa Hitzges, Pre-Kindergarten teacher at Stanley M. Makowski Early Childhood Center #99, was part of the pilot group that received intense training on this program. Melissa has witnessed firsthand the positive impact this curriculum has had on her Possible classroom resources/activities: students. Melissa particularly enjoys part of the ● “Day With No Math” program titled “Math Throughout the Year.” This by Marilyn Kaye (Author), Tim Bowers (Illustrator) component shows teachers how the concepts being ● “A Day Without Numbers” taught can be infused in everything they do Moderated by: Leisa Winrich throughout the day. Last year, Melissa and a fellow May 2018
http://www.globalclassroom.org/nonumb.html Pre-K colleague presented at an after school Math Professional Development for Pre-Kindergarten teachers. Melissa stated she “values the program’s ability to mold mathematical thinkers who, at four years of age, are able to explain their thinking.” With student understanding at the heart of each lesson, Building Blocks prepares students for the NYS Math Modules they will begin in Kindergarten. Building Blocks promotes a learning environment where math truly is EVERYWHERE!
English Language Arts Reading Department by: Dr. Julie Romain, Director by: Barbara Shea, Director & Jane Byrnes, Supervisor
The first iteration of The Common Core Learning Standards presented practices in mathematics. However, The Common Core Learning Standards in English Language Arts required teachers to infer the behavioral practices necessary in the classroom to Success in reading and math is considered achieve proficiency in the standards. The Next fundamental to educational success. Both reading Generation Learning Standards has designed a set and math require mastery of foundational skills to be of practices in both reading and writing for teachers applied automatically and fluently to achieve to use as a guide post when fostering academic academic proficiency through the grade levels. We behaviors among students. It is easy for one to think know that learners experiencing reading difficulty that math and ELA are subjects that are far apart. usually exhibit difficulty in math as well. Consider that Yet, in examining the practices required of students about 56 percent of children with reading disorders in each discipline, it is apparent that the two subjects have poor math achievement, and 43 percent of share common ground. Below is a chart listing math, students with a math disability have poor reading reading and writing practices. The practices that align skills. Math instruction can complement literacy skills are highlighted in the same color. While the practices and reading instruction can improve math. Math and do not align exactly, one can see that the reading may seem like an odd pair for a blended expectations for academic behavior in both subjects curriculum approach, but they actually do are not so different: complement each other. High-quality math instruction can improve literacy and future academic success. The importance of math on building literacy has been reported in many studies. Early learners Math Practices Reading and Writing Practices exposed to math instruction have better success in both reading and verbal communication skills. As · Make sense of · think, write, speak, and listen children talk about math, they build language and problems and to understand analytical skills. Children have to think about what words mean and determine how it applies to a May 2018
mathematical problem. Sorting, sequences, and persevere in · read often and widely from patterns that are learned in math education build solving them a range of global and diverse literacy skills in early learners. In addition, process · Reason texts skills needed for mathematics are similar to reading abstractly and · read for multiple purposes, skills and, when taught together, can reinforce each other. Examples of common skills are predicting, quantitatively including for learning and for inferring, communicating, comparing and contrasting, · Construct viable pleasure and recognizing cause and effect relationships. arguments and · self-select texts based on Moreover, the active practice of solving math problems can provide a natural means for increasing critique the interest and improving a student’s writing proficiency. In the reasoning of · persevere through process of writing, students clarify their own others challenging, complex texts understanding of mathematics by organizing their ideas and thoughts logically and structuring · Model with · enrich personal language, conclusions in a coherent way. Therefore, the mathematics background knowledge, and importance of writing in the mathematics classroom · Use vocabulary through reading cannot be stressed enough. appropriate tools and communicating with Reading, writing, and mathematics are, and should be, inseparable. Teachers who recognize the strategically. others interrelatedness of mathematics and literacy can · Attend to · monitor comprehension and design instruction that reflects these similarities and precision. apply reading strategies enhances the opportunity for academic success.
· Look for and flexibly make use of · make connections (to self, structure other texts, ideas, cultures, eras, etc.) · think, read, speak, and listen to support writing · write often and widely in a variety of formats, using print and digital resources and tools · write for multiple purposes, including for learning and for pleasure · persevere through challenging writing tasks · enrich personal language, background knowledge, and vocabulary through writing and communicating with others · experiment and play with language May 2018
· analyze mentor texts to enhance writing · strengthen writing by planning, revising, editing, rewriting, or trying a new approach
Library Services Science by: Michael Cambria by: Kelly Baudo, Director of Science
Math: The Building Blocks of Libraries Libraries use classification systems to organize the The Connection Between Math and Science books on the shelves. A classification system uses Math plays more of a role in our lives than many letters and/or numbers (call numbers) to arrange the people realize. Math is also a huge part your books so that books on the same topic are together. students’ studies in science. Although science may appear to be quite a different subject, the study of Libraries in the United States generally use either the math can ultimately help kids understand concepts in Library of Congress Classification System (LC) or the science. Mathematics and science have a long and Dewey Decimal Classification System to organize close relationship that is of crucial and growing their books. Most academic libraries use LC, and most importance for both. “Mathematics is an intrinsic component of science, part of its fabric, its universal public libraries and K-12 school libraries use Dewey. language and indispensable source of intellectual Decoding Dewey Decimal Call Numbers tools. Reciprocally, science inspires and stimulates mathematics, posing new questions, engendering Main 800 Literature new ways of thinking, and ultimately conditioning the Class value system of mathematics.” (National Science Foundation) Division 810 American literature in English The ability to accurately determine calculations or scientific principles is largely the result of the Section 813 American fiction in English relationship between math and science. Science applies both simple and complex mathematical 813.54 ...further narrowing of topic concepts, such as measuring the amount of chemicals to use in a solution or figuring out the 813.54 M37 Cutter Number identifying author’ velocity required in order for the Mars Curiosity to name safely land on Mars. At its most basic, math is a tool that reinforces scientific theories; at its most complex, 813.54 M37 Edition date it can be a driving force that powers scientific 2007 discovery. Math can reveal and relate what students May 2018
discover in an experiment; helping them find relationships between an experiment’s hypothesis The Dewey Decimal Classification (DDC) system is a and the data that is collected. By using a math general knowledge organization tool that is formula, students can use data as evidence to either continuously revised to keep pace with knowledge. support or dispute their original theories. Without the The system was conceived by Melvil Dewey in 1873 application of math in this regard, proving or and was first published in 1876. The DDC is the most disproving scientific theories would be impossible. widely used classification system in the world. Libraries in more than 135 countries use the DDC to “Fields such as physics and electrical organize and provide access to their collections, and engineering that have always been DDC numbers are featured in the national mathematical are becoming even more so. bibliographies of more than 60 countries. Libraries of Sciences that have not been heavily every type apply Dewey numbers on a daily basis and mathematical in the past, for example, biology, physiology, and medicine are share these numbers through a variety of means. The moving from description and taxonomy to DDC is built on sound principles that make it ideal as analysis and explanation; many of their a general knowledge organization tool problems involve systems that are only In the DDC, basic classes are organized by disciplines partially understood and are therefore inherently uncertain, demanding or fields of study. At the broadest level, the DDC is exploration with new mathematical tools. divided into ten main classes, which together cover the Progress in science, in all its branches, entire world of knowledge. Each main class is further requires close involvement and divided into ten divisions, and each division into ten strengthening of the mathematical sections. enterprise; new science and new mathematics go hand in hand.” (Division The first summary contains the ten main classes. The of Mathematical Science National Science first digit in each three-digit number represents the Foundation) main class. For example, 600 represents technology. The second summary contains the hundred divisions. Math and Science as part of the STEM field The second digit in each three-digit number indicates Many times when you hear the words math and science the division. For example, 600 is used for general together you automatically think of STEM (Science, works on technology, 610 for medicine and health, Technology, Engineering and Math) or STEM education. What is STEM Education? STEM Education is a 620 for engineering and 630 for agriculture. curriculum based on the idea of educating students in four The third summary contains the thousand sections. specific disciplines: science, technology, engineering and The third digit in each three-digit number indicates the mathematics; in an interdisciplinary and applied approach. section. Thus, 610 is used for general works on Rather than instructing the four disciplines as separate and medicine and health, 611 for human anatomy, 612 for discrete subjects, STEM integrates them into a cohesive learning paradigm based on real-world applications. What human physiology and 613 for personal health and separates STEM from the traditional science and math safety. education is the blended learning environment and Arabic numerals are used to represent each class in the showing students how the scientific method can be applied DDC. A decimal point follows the third digit in a class to everyday life. It teaches students computational thinking and focuses on the real world applications of problem number, after which division by ten continues to the May 2018 specific degree of classification needed. solving.
The Ten Main Classes 000 Computer science, information & general works
100 Philosophy & psychology
200 Religion
300 Social sciences
400 Language
500 Science
600 Technology
700 Arts & recreation
800 Literature
900 History & geography
A major objective of libraries is to ensure that optimum use is made of their collections by leading each user as directly as possible to the material he or she requires. As an aide to the achievement towards this objective almost all libraries find it helpful and necessary to impose upon their books and other material one or more forms of subject control. Through the use of mathematics, librarians have control.
Social Studies
Math is everywhere across the globe, take a look at Mathematics through the eyes of historians. As the Greek empire began to spread its sphere of influence into Asia Minor, Mesopotamia and beyond, the Greeks were smart enough to adopt and adapt useful elements from the societies they conquered. This was as true of their mathematics as anything else, and they adopted elements of mathematics from both the Babylonians and the Egyptians. But they soon started to make important contributions in their own right and, for the first time, we can acknowledge contributions by individuals. By the Hellenistic period, the Greeks had presided over one of the most dramatic and important revolutions in mathematical thought of all time. The ancient Greek numeral system, known as Attic or Herodianic numerals, was fully developed by about 450 BCE, and in regular use possibly as early as the 7th Century BCE. It was a base 10 system similar to the earlier Egyptian one (and May 2018 even more similar to the later Roman system), with symbols for 1, 5, 10, 50, 100, 500 and 1,000 repeated as many times needed to represent the desired number. Addition was done by totaling separately the symbols (1s, 10s, 100s, etc.) in the numbers to be added, and multiplication was a laborious process based on successive doublings (division was based on the inverse of this process).
But most of Greek mathematics was based on geometry. Thales, one of the Seven Sages of Ancient Greece, who lived on the Ionian coast of Asian Minor in the first half of the 6th Century BCE, is usually considered to have been the first to lay down guidelines for the abstract development of geometry, although what we know of his work (such as on similar and right triangles) now seems quite elementary.
The advent of the printing press in the mid-15th Century also had a huge impact. Numerous books on arithmetic were published for the purpose of teaching business people computational methods for their commercial needs and mathematics gradually began to acquire a more important position in education.
Europe’s first great medieval mathematician was the Italian Leonardo of Pisa, better known by his nickname Fibonacci. Although best known for the so-called Fibonacci Sequence of numbers, perhaps his most important contribution to European mathematics was his role in spreading the use of the Hindu-Arabic numeral system throughout Europe early in the 13th Century, which soon made the Roman numeral system obsolete, and opened the way for great advances in European mathematics.
Source: http://www.storyofmathematics.com
Art Education Music Education by: Michele Agosto, Supervisor by: James Schwanz, Supervisor ART & MATH... Math and Music: It’s More Than What Vibrates in Your Ear OPPOSITES ATTRACT! Art and Math may seem at opposing sides of the It’s often been said that music and math are intertwined, academic world- the analytical vs. the abstract, the but for casual listeners and those who are unfamiliar with rational vs. the conceptual. However, patterns, angles music for its full range of technical, theoretical and lines, and deep cognition are what connects these two expressive properties, it may be challenging to understand areas in very practical, complex and fascinating ways. the undeniable relationships between music and math. Basic things, like measuring lines are certainly Dating back to the ancient civilized cultures of the Greeks, Egyptians, Indians and Chinese, the study of the math-related, but the intricacies of creating art can often relationship between music and math has intrigued humans be described through mathematics. Additionally, when for hundreds of years. these disciplines are combined and interwoven with skill, students’ reach higher levels of Bloom’s Taxonomy “It was Pythagoras who realized that and apply thinking in all sorts of amazing, creative ways. different sounds can be made with
different weights and vibrations. This ARTISTS WHO USE MATH led to his discovery that the pitch of a vibrating string is proportional to and can be controlled by its length. Strings May 2018
Leonardo da Vinci that are halved in length are one octave higher than the The Mona Lisa, painted by Leonardo da Vinci, is drawn original. In essence, the shorter the string, the higher the according to the Golden Ratio. The Golden Ratio in pitch. He also realized that notes of certain frequencies math terms is 1:0.618 and has been coined “golden” sound best with multiple frequencies of that note. For because it is said to be the sweet spot for pleasing example, a note of 220Hz sounds best with notes of aesthetics. The golden ratio, or golden proportion, can 440Hz, 660Hz, and so on (Music, Math, and Pattern).” be found throughout the human body, and in art is replicated in what is called a “golden rectangle”. This is When we listen to music, we are generally unaware of the intricate and complex cognitive process that’s involved with simply a rectangle with dimensions that reflect the the processing of sound waves. In an article from Kent golden ratio. The Mona Lisa has many golden State University, “when a note is played, sound waves rectangles throughout the painting. By drawing a travel from an instrument or amplifier and reverberates on rectangle around her face, we can see that it indeed our eardrums, and it’s the frequency of this sound wave meets the golden that tells our brain which pitch or note is being played.” proportion. If we divide that rectangle with a line In a 2009 article written by Arvind Gupta for the Vancouver drawn across her eyes, we Sun, he discussed the mathematical connection between get another golden music’s popularity in the mainstream due to some songs rectangle, meaning that the mathematical structure, “Pachelbel’s Canon in D…is said to proportion of her head reach the masses because of its repetitive structure, a trend length to her eyes meets very apparent in music today. No doubt the amazing the golden ratio. You will popularity of hip-hop music, with its rhythmic beats and find other golden looping breaks, is partially due to our innate mathematical rectangles that can be need for rhythm and patterns…Understanding sound drawn on the rest of her waves, particularly the difference between octave notes, body, such as from the neck to the top of her hands. requires a bit of mathematics and physics.” M.C. Escher Listen/Watch here: https://www.youtube.com/watch?v=JvNQLJ1_HQ0 Escher’s art can be found on all sorts of popular and practical items- from mugs to t-shirts- and everyone In a 2006 article written for the Educational Psychologist by seems to love how he challenged the optical with the Dr. Frances Rauscher she explains, “young children mathematical. M.C. Escher used only simple drawing provided with instrumental instruction score significantly tools and the naked eye to create stunning higher on tasks measuring spatial-temporal cognition, mathematical pieces. He focused on the division of the hand-eye coordination and arithmetic…A literate musician is plane and played with impossible spaces. He produced required to continually mentally subdivide beat to arrive at polytypes in drawings, which cannot be constructed in the correct interpretation of rhythmic notation…The context the real world, but can be has changed, but the structure of the problem is essentially described using the same as any part-whole problem posed mathematics. Escher’s mathematically.” drawings looked possible by perception, but were Lastly, the connections between music theory and math mathematically impossible. can appear vast and complex, so to help, here are a few The drawing to the left simple ways to examine the relationship between basic called Relativity, was one of music theory and math in the classroom. For the purpose his many masterpieces, of this article, we’ll examine one of the most recognizable where he has created a music themes in music history, Ludwig Van Beethoven’s theme from Symphony No. 9, also recognized as “Ode to staircase that continues to ascend and descend- Joy” in order to gain a better understanding of: obviously mathematically impossible, but the drawing makes this optical illusion seem highly realistic. 1. The duration of note values; and May 2018
2. Examining compositions to better understand There are several contemporary artists that use fractions and bar lines. technology to create incredible fractal artworks that are truly mind-blowing. For a look at who they are and what they are doing, make sure to check this link out.
In art, mathematics is not always visible, unless you are aware of its existence. There is much symmetry, geometry, and measurement (which include angles, perspective and scale) used by artists to create art. There are many artists that take advantage of mathematical findings and formulas to create art that is realistic, awe- inspiring, and beautiful...proving that math and art are quite intricately and exquisitely linked. Who knew? :) More on ART & MATH? Check out these links! Penrose Tiling
Links to Art & Math connections that you can use in the Art, Math and Science classrooms
Why the history of math is also the history of art
Math and art: the good, the bad and the ugly
May 2018
By: Pietro Mendola, Supervisor World Languages Department The focus of this month's newsletter is "Math is Everywhere." Math concepts appear frequently in the World Languages curriculum. The New York State World Languages Topics such as Personal Identification, Shopping, Health and Welfare, and Travel connect with Math. In this article, I will share with you where those connections may appear and some areas of focus for lesson planning.
Personal Identification: This topic focuses on biographical information. Students learn how to communicate their age, date of birth, height, weight etc. Mathematical connection to this topic can be numbers and measurement conversion of height and weight.
Shopping: This topic focuses on where to go to purchase certain items. Mathematical connection to this topic can be the price of an item, currency used in the target language country, currency conversion (Euros, Pesos, Renminbi) and measurement conversion regarding size (shoe size etc.).
Health and Welfare: This topic focuses on a student’s ability to communicate his or her state of health and understand medical advice. Mathematical connections are numbers (how many pills to take), measurement conversion (body temperature – fever) May 2018
Travel: This topic focuses on making travel plans, vocabulary essential for travel days and schedules or timetables. Some mathematical connections are reading and understanding travel itineraries, currency and currency conversion, weather conditions (Centigrade versus Fahrenheit).
In conclusion, when lesson planning it is recommended that practitioners take a close look at the topic being taught to identify common threads to link them to Math and capitalize instruction. Below you will find links to the Buffalo Public Schools World Languages Curriculum, The Office of Bilingual Education and World Languages LOTE Topics and Learning Standards. You are encouraged to use these resources when planning lessons.
Links
Buffalo Public Schools World Languages Curriculum: https://ny01913551.schoolwires.net/Page/5125. Office of Bilingual Education and World Languages LOTE Topics and Learning Standards: http://www.nysed.gov/program-offices/office-bilingual-education-and-world-languages-obewl.
May 2018
Physical Education by: Andrea Norton
The theme of this month’s newsletter, ‘Math is Everywhere’ certainly applies to Physical Education. Numerous activities in PE from K-12th grade support the learning of math concepts, and in turn, math concepts help students learn Physical Education skills and concepts. PE and sport is math in an applied form! Physical Educators help students apply math in all grades when they create groups of students - having students count off and in as simple things as dividing into odd and even groups to transition to a new activity.
Physical Educators may start with supporting learning of basic math in the primary grades where students doing warm ups practice counting, skip counting, and multiplication while doing jumping jacks or curl ups. To teach student about the positive effects of exercise, PE teachers help students learn how to calculate their resting and target heart rates and Body Mass Index.
These skills continue to grow and be used as students are tested through FITNESSGRAM on the health related components of Cardiovascular Fitness, Muscular Strength, Muscular Endurance, Flexibility and Body Composition to determine if they are in the ‘Healthy Fitness Zone’ for their age and gender.
Students compare their own personal results to the standardized charts and can set personal goals to improve. Secondary students can utilize this information to create a personal fitness plan and create charts or graphs showing their improvement. Teachers also can create graphs detailing either individual or class progress when counting laps or steps to travel the length of the Erie Canal, across the USA or to some other geographical point that might be related to another subject’s content.
The application of math skills in PE go on and on. From the variety of scoring systems in sports, following sequences and patterns, estimating and measuring time and distance in events like track and swimming, determining angles for passing or shooting, diagraming fields or courts, to tracking and analyzing individual and team statistics it is evident that Math is everywhere in Physical Education. Therefore, helping students develop their Math during PE sessions not only helps them in the classroom but also helps the student in PE. Applying Math in physical situations can help transform a student’s attitude and perception of competence. http://learning.gaa.ie/sites/default/files/Integrating%20Maths%20and%20PE%20%28Sean%20Delaney%20IPPEA%202012%29l.pdf https://www.tandfonline.com/doi/abs/10.1080/08924562.2004.10591122?src=recsys https://www.tandfonline.com/doi/abs/10.1080/07303084.2004.10608541?src=recsys