Anne Marie Marshall, PhD Lehman College CUNY

1. Making Connections Between Mathematics and Music: prospective Teachers’ Experiencing the Mathematics in DrummingNCTM Regional ConferenceBaltimore, MD Anne Marie Marshall, PhD Lehman College CUNY Ryan Bazinet, PhD John Jay College CUNY

2. WELOME! Introductions Our story The lesson Do some drumming! What “we” learned Questions and conversations

3. Turn and Talk How are mathematics and music connected?

4. EDE 715: Children’s Concepts of Mathematics in Grades 1-6 Exploration of the ways that children develop an understanding of mathematical literacies in family, neighborhood, and school settings. Approaches to formal and informal documentation and assessment of children’s development in mathematics. Use of media and technology as appropriate within an integrated curriculum. Fieldwork in early childhood settings with diverse populations, integrative seminar, development of an academic portfolio.

5. Mathematics in the Community Unit In peer groups, you will be asked to identify a setting outside of the classroom that would provide a meaningful context for students to explore mathematics. This could be, but is not limited to, a museum, community based center or cultural organization. Visit the site and create an integrated mathematics unit that situates the trip, and describe how the context and mathematics would be relevant to students. Mathematics must be in accord with the Common Core State Standards and to students living in a large urban community.

6. The Unit • Phase 1: Prepare for and attend the trip • Site selection • Pre-visit prep (web, coordinators/docents) • Logistics (accommodations, travel, cost) • Rationale • Phase 2: Planning the unit • 5-day unit • Integrated content • 1 Fieldtrip

7. Rationale for the Assignment • Connections across content, across disciplines -NCTM Connections Process Standard. 2. Ethnomathematics / Culturally relevant -mathematics is not a culture-free discipline 3. Understanding mathematics in a different way -when mathematics is placed in a relevant context, it has meaning for students. 4. Preparing for changing state of schools, loss of specialists -arts education is being challenged by budget cuts and ]as pressure to improve test scores in “core” subjects. 

8. Integrating content in the classroom Research indicates that using an interdisciplinary curriculum provides opportunities for more relevant, less fragmented, and more stimulating experiences for learners (Frykholm & Glasson, 2005; Koirala & Bowman, 2003).

9. In the past, units have included... Trips to Pizzerias (measurement, fractions) (Students will watch chefs make pizza, Celebrate with pizza) Trips to Grocery Stores/Corner Stores (money) (Students will receive $ and need to purchase food for a party) Trips to the Park (looking for shapes) (Take a shape walk through the park to see as many shapes as possible) Trips to the Zoo (collecting data, story problems) (Keep track of how many zebras, monkeys, elephants you see. Create story problems) But the integration has been superficial. So….

10. Our Study Questions How does experiencing an integrated lesson impact prospective teachers’ understanding of content and how to integrate curriculum? What are necessary components of learning about integrating curriculum that help support transfer to practice? Which are the most important?

11. The Study… 1 mathematics educator, 1 ethnomusicologist Co-teach an integrated math/music lesson, focusing on points in the lesson where math and music are integrated After the lesson, students reflected on the experience and students created integrated math/music lessons Integrated Lesson Student reflections

12. The Math and Drumming Lesson Who has ever played an instrument? In what ways do you think math and music are related? Listen to examples of drumming Drumming Notation- Mathematics Students play drums Reflection on the experience

13. Turn and Talk What are all the ways math and music are connected? How does music use math?

14. How are mathematics and music connected? Students said… Timing- counting beats Adding/taking away beats Patterns Grouping Measuring how long to play a beat Symbols Adding/subtracting BPM (beats per min) rate

15. Listen… What do you notice about the drumming in each song? Try to describe the beats and rhythms you hear in each song. How does the music make you feel?

16. EXAMPLE A

17. EXAMPLE B

18. EXAMPLE C

19. Example A: Indonesia

20. Example B: Nigeria

21. Example C: Zuccotti Park

22. Turn and Talk Why do you think different songs sound different? In what ways do drums make songs sound different? How can you describe how drumming is different in different songs?

23. How could you represent the beats in a song?

25. Western Notation

26. TUBS Notation Time Unit Box System Pa pa do / gun gun ta / go do pa do / go ta go do

27. What’s a Polyrhythm? Polyrhythms are produced by dividing a measure in two or more different ways simultaneously and are related to fractions and the least common multiple/greatest common divisor. For example, if one drum is to play 3equal beats in the same space of time, as another drum is to play 2equal beats, we must divide the measure up into 6beats (or a multiple of 6). This division of 6beats between 2 drums has clear connections to understanding and experiencing factors, multiples, and fractions.

28. Visual Representation of 3 against 2 Polyrhythm

29. Polyrhythm Exercise Bell Pattern: kon kon ko - lo kon ko - lo Triple Pattern: 3 + 3 + 3 + 3 + Duple Pattern: 2 + 2 + 2 + 2 + 2 + 2 +

30. How are mathematics and music connected? Students said… Timing- counting beats Adding/taking away beats Patterns Grouping Measuring how long to play a beat Time signature Pitch Loudness Symbols Shape Adding/subtracting Size BPM (beats per min)/rate Magnitude Fractions Part/whole Multiplication Division Notation Factors

31. Homework: 1. Complete a reflection 2. Design a lesson that includes the integration of music and mathematics. You can choose to highlight any of the areas we talked about this afternoonor use any new ideas you may have.

32. Q1: What did you learn about math and music?Students responded… new techniques to incorporate math and music learned about other cultures/music from other cultures math is a subject in life, it is related to everything incorporate math in fun and meaningful ways integrating math and other subjects makes students think about math in the real world gives them practical approaches to learning and using mathematics helps students to answer the question “When are we ever going to use this?” helps students enjoy math math lives everywhere segments and counting is what actually gives us music music is not just sound. It is organized. It takes knowledge. It has length, speed, intensity. I was surprised to see that Math and Music have so much in common. I learned that as much as I listen to music on a daily basis, I really don’t know anything about it. math and music have patterns, shape, symbols, notation Music uses fractions, parts & wholes language of drumming easier to integrate subjects than I previously had thought I learned about drum circles and what they are used for.

33. Q2: What did you learn about integrating subjects?Students responded… best way is through an interactive lesson it is important to let students speak about what they already know and then work with that as a foundation. there are many ways to integrate math and other subjects easy to find ways that math can be integrated with different disciplines integrating math and another discipline can make math more enjoyable for those who do not ‘like’ math

34. Q3: What new questions do you have?Students responded… What would be the next step after this lesson? What other areas can music be integrated with? How can you utilize instruments if you have little or no access to them? When integrating math and other subjections, how would you assess the students? Would this have been an easy lesson to do with only one instructor instead of two?

35. Lessons Included Students will sing ‘Twinkle Twinkle Little Star” to look at patterns Students will show how words repeat (patterns) in “Bah Bah Black Sheep” Students will use measures to connect notes to fractions (whole note, half note, quarter note, etc) But…. Students will listen to a song about shapes on YouTube and then talk about shapes Students will listen to an audio tape song connected with the book, “One Elephant Went Out to Play” Students will sing “The Hokey Pokey” while ‘putting in a shape’

36. Now what? How does experiencing an integrated lesson impact prospective teachers’ understanding of content and how to integrate curriculum? What are necessary components of learning about integrating curriculum that help support transfer to practice? Which are the most important?

37. Questions and CommentsThank you! Anne Marie Marshall anne.marshall@lehman.cuny.edu Ryan Bazinet rbazinet@jjay.cuny.edu