Spontaneous Reflections on Teaching Musical Math

1. Spontaneous Reflections on Teaching Musical Math Dawn’s jottings: opinions and findings

2. “FOURTH VS QUARTER” • Although “fourth” and “quarter” can be used interchangeably, this creates confusion in children when discussing “quarter notes”, “quarter hour”, “quarter of a pizza”, and WOW…“fourth quarter of the game”, etc. Math teachers in our district use, “fourth” for “quarter”. • Children do not automatically equate the words “fourth and “quarter”. I have had to remind them repeatedly, slowing down my teaching progress. Therefore, I strongly support teaching “quarter” as a noun and “fourth” as an ordinal number in the early grades until the CONCEPT of “1/4” in relationship to the whole and its parts isthoroughly understood. • Using “quarter” more in math lingo will help in reinforcing the money system, time relationships and with measurement. • To a musician, this difference is CRUCIAL as the two terms have VERY DIFFERENT meanings. A “fourth” means the “interval” or distance between two notes, whereas a “quarter” represents a specific rhythmic notation. • At the very least, the terms should be dually taught by elementary and middle school teachers. • Results of spending a weekend interviewing people I met in Genesee County revealed the use of “quarter” was almost universal in everyday lingo from pizza, to baking, to carpentry. Fourth meant “fourth in line”. • SUGGESTION: Find out which term your school’s math department is using and share this information with them. Maybe they can help.

3. “Quarter” Examples • from the Cambridge Advanced Learner's Dictionary • 1.one of four equal parts of something; ¼: • He cut the orange into quarters. • Under a quarter of peoplequestioned said that they were happilymarried. • My house is situated a mile and three-quarters from here. • a quarter of an hour › 15 minutes “I'll meet you at a quarter past five”. • 2.one of four periods of time into which a year is divided for financialcalculations, suchas for profits or taxes: There was a fall in unemployment in the second quarter of the year. I get an electricitybill every quarter. › • 3.one of four periods in a game of American football and other ballsports “Fourth” Examples • Fourth on the grid. • In the fourth quarter of 2001, the number of actions entered was just over 17 % less than the fourth quarter of 2001 • Tom Richards also finished fourth in both his finals. • Fourth in the discus with 25.8m. • Fourth from the right, this will bring up your address book. • Fourth edition of the Code was published in October 2000. • Fourth century, • Fourth of July

4. TEACHING FRACTIONAL CORE MATH USING THE TIME SIGNATURE Reasoning: asking my entire student base (who have been through 5-6 years of quality general music instruction) to explain a time signature yielded a variety of answers: • “The top number means how many notes are in a measure.” • “The top number means how many beats are in the piece.” • “I forgot what the bottom number means.” • “The bottom number means how many beats are in a measure.” In other words, “I don’t know what a time signature is instructing me to do.” SO, I decided to make the time signature into an easily understood command. SUGGESTION: Do not teach the time signature as two separate numbers. SUGGESTION: Use terms “Walking, Jogging, Running” and “Walking beat, Jogging beat, Running beat.” This helps students understand that beat values and feels can change depending on the demands of the music. Take time to establish these when beginning a piece and review them briefly each time just to reinforce the concept.

5. To start incorporating CORE MATH into your teaching consider that the time signature is actually a fraction. This opens up interesting musical math opportunities! “Count three walking quarter notes in every measure.” Extended explanation: “Sometimes these walking notes are hiding inside bigger notes. Sometimes smaller jogging or running notes combine to create one big walking note.” “Count six walking eighth notes in every measure” “Count four walking half notes in every measure.”

6. IN BAND LESSONS • We establish the walking beat of the target piece and overview the jogging and (if needed) running note values. • We always break dotted rhythms into 3 EQUAL LESSER PARTS. Never 1 ½ value! Musicians SHOULD DECOMPOSE (SUBDIVIDE). Once you assign an absolute value to the dot…(like “in the dotted quarter the dot adds ONE extra beat” the student often makes this the golden rule and doesn’t understand when it changes! You will have twice the work when you then have to re-teach the larger concept. (Show “dotted monster”) • Students can draw all or part of the hierarchy of notes chart. • Possible Learning Targets: I can convert musical notes to their fractional equivalents. I can give two examples of how note values decompose into smaller notes I can solve a musical math problem using mathematical proof. I can give one reason why understanding note values can help me understand fractional math.

7. If I were to go back to the elementary general music classroom I would try to weight my teaching emphasis differently. • I would teach: “Notes walk, jog, and run” (Extended explanation: “Notes can sit or sleep.”) I might use the terms: “bigger beat, smaller beat” and would discuss this with my department and agree on a common lingo. Example: “Sometimes the small beat has to run so fast that he finds it easier to ride on a bigger beat. AND “Sometimes a big beat walks SO slow that the tiny beat gets bored riding and decides to walk alongside. We would act this out, switching between the “big feel” and the “little feel”, or “walking, jogging, running” feel. • I would teach that ANY of these notes can walk, jog, or run (just like any size animal can walk, jog or run) I would spend LOTS of time doing MOVEMENT activities with different sized notes (objects, animals, cartoon characters… ) walking, jogging, or running alone and/or in relationship to each other. I would use whatever counting system I liked, but by the year students entered band I would be in collaboration with the band director. Students will adapt and have two methods to fall back on.

8. I would teach the names of the notes: Whole, Half, Quarter, Eighth (Grade 3 or 4: sixteenths) • I would teach these in conjunction with a hands on pie on my wall made out of Velcro sections and emphasize the mathematical parts of a whole from the very beginning. “If wholes walk, halves jog.” Yes I would begin with the WHOLE NOTE in KINDERGARTEN rather than the QUARTER. I would use common everyday objects to show these relationships: townhouses/ranch houses, trees/bushes, tigers/house cats • I would search out songs with “whole, half, etc. in them. • I would include math speak: “quarter” of an hour; “half” of this vibrating string; a “whole” glass of water to tap and I would visually demonstrate these things, giving lots of hands- on. • When students began to actually READ music (not just look at books for the words) I would use FINALE and deliberately change some favorite simple songs into different time signatures.

9. We would COMPOSE/IMPROVISE music (written and by rote) using walking, jogging and running. They pick their favorite value to walk of COURSE. • I would AVOID total emphasis on the quarter note getting the beat. This causes many math students to assign the value “1” (which is a WHOLE) to the QUARTER NOTE • I would AVOID doing simple math problems using beat values in the general music class until students understood different the concept of different denominators in the time signature. (How many of us did hundreds of these in the past in the name of supporting math? My hand is up high!) • I would INSTEAD do note relationship math: “How many quarter notes are in a whole note?” . “How many sixteenth notes does a half note break into?” • A dotted value represents THREE of the next note in the hierarchy It’s hard, if not impossible, to tap 1 ½ beats (complex beat relationships) Its much easier to understand and tap three walking, jogging, or running beats

10. If I found myself wondering if I was helping or hurting having to expand upon a concept later … “Kids can’t understand this at this young age so I’ll only teach one part of it” … and I couldn’t figure out a creative way to make it grow for them, I might choose to AVOID it rather than ENGRAVE one inflexible facet of it on their minds.

11. Future project ideas: 1. Relate musical note divisions to a ruler: whole note= 1 inch and measure things. Have their measurements lead them to a hidden piece of candy or object. 2. DREAM PROJECT: Collaborate with tech and science teachers to build a giant PVC tubulum (Blue man group) or a smaller version. Do this with a group of kids for an extra project and have them measure the parts from the plans using note relationships/measurement values.