Digital music math: technology as a STEM teaching tool

for Aboriginal students

Joyce VAN DE VEGTE

Electronics & Computer Engineering Technology

Camosun College Victoria, BC, Canada

vandevegte@camosun.ca

ABSTRACT A series of learning units was developed as a high-interest STEM teaching tool for a group of Aboriginal high school students. The units integrated e-learning, classroom learning and technology in a way designed to spark interest in subject matter, and to help students see links between mathematics and engineering and the real world. The series, entitled “Digital Music Math,” culminated in a field trip to the local college to construct an electronic game, and each learning unit was connected in a material way to this final project. Keywords: e-learning, STEM, digital music, math, Aboriginal, First Nations

1. INTRODUCTION Teachers often lament how difficult it is to convince students that math is useful. Many students cannot see past rows of times tables and right-angled triangles to anything that pertains to their own lives. In this regard, Aboriginal students are no different from non-Aboriginal students. Where Aboriginal students do differ from their non-Aboriginal peers is in their numeracy, reading and writing scores, and their high school graduation rates. The Fraser Institute’s 2011 Report Card on Aboriginal Education in British Columbia, for example, reports that Aboriginal students score 15% to 20% lower than average on standardized tests, and experience delays in advancement on average twice as often [1]. These statistics are of course not an indictment of student performance but rather an indication of how poorly the education system serves Aboriginal students. In Canada, high school dropouts are more likely to live in poverty, are 2.5 times more likely to be unemployed, receive 85% of government welfare spending, and form 80% of the population of federal jails [2]. The urgent need to find better ways to connect with Aboriginal high school students is manifest when this information is paired with a few additional statistics: 40% of Aboriginals aged 20 to

24 and 32% aged 25 to 44 lack high school certification, while only 10% of non-Aboriginals aged 20 to 44 do [3]. The federal government is beginning to recognize the importance of the science, technology, engineering and mathematics (STEM) dimensions of this issue in particular. In December 2012, new funding was announced for the Indigenous Education Coalition (IEC), through the Federal Economic Development Agency for Southern Ontario, specifically for the purpose of providing innovative STEM training to First Nations and other Aboriginal students [4]. As Nicol et al have observed, “school mathematics has often functioned to exclude Aboriginal students and others from advanced studies of mathematics” [5]. The work described in this paper began as a challenge to engage and motivate Grade 7 to 11 students at the LÁU,WELNEW Tribal School in Brentwood Bay, BC, in their mathematics and technology studies. Ten male and five female students participated in the pilot project.

2. PLANNING PARTNERS Cora Oliver, a Grade 10 teacher at the LÁU,WELNEW Tribal School, was able to provide essential information about her students’ backgrounds and abilities. She arranged for both classroom and laboratory space to be available at the Tribal School for all meetings, and reviewed proposed teaching materials to assess their suitability. Cora was also a teaching partner in all activities. A local employer and strong community supporter, Schneider Electric, agreed to provide printed circuit boards and electronic components for the project.

3. LEARNING STRUCTURE AND TOOLS Learning units were designed around a final project, an electronic musical memory game, to be constructed

during a field trip visit to Camosun College. The hope was that the promise of a field trip and the idea of soldering and programming an electronic device would be motivating and would help to maintain student interest in the subject matter. To this end, each two-hour lesson was linked in some way to the electronic game the students would build. An outline of the lessons is provided in Table 1. Electronic musical memory game The game circuit is depicted in Figure 1. The game is driven by a PIC microcontroller. A short musical introduction is played with a speaker, after which a single LED lights, accompanied by a tone. If the player presses the correct button, the microcontroller proceeds with a sequence of two LEDs and tones. As the player faithfully reproduces the required patterns, the sequences lengthen. A high score produces a short happy tune; a mistake produces a short sad tune.

The musical memory game requires the soldering of electronic components onto a printed circuit board, as well as the programming of the PIC microcontroller that controls the game’s operation. Digital audio software The digital audio editor Audacity [6] was used to support the lessons. With a bit of guidance, the interface was fairly straightforward for the students to operate. Within the Audacity environment, students were able to record sounds from tuning forks and also their own voices, and then study the shapes of both the signals and their spectra. Audacity could also generate signals such as chirps, noise and tones, and cursors allowed users to make measurements.

Lesson Title Location Lesson Activities

Lesson 1 Sound Lab � discuss the concepts of sound, frequency and spectrum � calculate the frequency of a repeating wave � use digital audio software to examine the signals and spectra for

tuning fork and voice sounds

Lesson 2 Sine waves Classroom � discuss the concepts of amplitude and period � relate period and frequency

Lesson 3 Music notes Lab � relate piano notes and frequency using an online piano � use digital audio software to examine piano note signals and spectra � identify harmonics � compare frequencies of piano notes

Lesson 4 MP3 and compression

Classroom � discuss digital images, pixels and the concept of compression � calculate compression ratio � listen for differences between CDA/MP3 versions of the same song � calculate how many songs can be stored in an iPod Touch in CDA or

MP3 format

Lesson 5 Programming concepts

Lab � the concept of a computer program and a programming language � view the C program for the musical memory game � identify the parts of the program that determine the songs and notes

played � use an online piano to connect notes in the computer program to

sounds

Lesson 6 Your own song Classroom/Lab � write a sequence of notes in the format required by the computer program to play a song selected or composed by the student

� introduce musical notation and link to computer program notation

Lesson 7 LEDs, resistors, and other electronic parts

Lab � introduce the electronic circuit components needed for the musical memory game

� use metric prefixes � interpret resistor colour codes � measure resistance using a multimeter � introduce the breadboard for circuit construction

Lesson 8 Building an LED circuit

Lab � determine the correct resistor to pair with an LED of a particular colour

� build an LED and resistor circuit on a breadboard � measure voltage using a multimeter

Lesson 9 Field trip

(6 hours)

College Lab � select electronic parts � solder parts to a printed circuit board � personalize the songs in a computer program � program a microcontroller � test the electronic musical memory game

Table 1. The lessons.

Figure 1. Electronic musical memory game. Figure 2 shows what the Audacity screen looks like and Figure 3 gives an example of a spectrum for a spoken “ooo” sound. Real-time interaction with signals is a great strength of Audacity as a tool for learning. Once they have mastered the simple record procedure, students can quickly and easily experiment with all manner of sounds, even goofy ones. Moreover, none of the students had previously conceived of the idea that his or her own voice was linked to the time-varying waveform observed on the screen. The digital music math lessons exploited only a small fraction of the capabilities of the software and, because it was freely available, students could continue to use it beyond the end of the project, at school or at home, to experiment with other features.

Figure 2. Sample Audacity screen for “ooo” sound

Figure 3. Audacity spectrum for “ooo” sound

Online piano Figure 4 shows a screenshot of the online piano used in the lessons, another free resource [7]. Very few of the students had experience playing the piano, so the online instrument was a favoured element. With both Audacity and the online piano running, students were able to record piano notes and study the signals and spectra in real time.

Figure 4. Online piano.

Later in the lesson series, students used the online piano to invent a song. The labelling of the keys according to note and octave allowed a relatively simple translation between the song being played and the computer program code that would enable the same song to be played in the electronic musical memory game. Integrating related ideas about music notes from several sources permitted students to gain confidence with the technology. They could play and hear a note, see what the signal looked like in Audacity, view where the note’s code (e.g. C3) appeared in the computer program, and link the note they were hearing to its representation in formal musical notation. Digital music and MP3 compression Music is intensely interesting to most high school students. Many of them carry digital music players. Very few have ever considered how the songs they listen to are stored. The basic ideas behind MP3 compression are appealing and easy for students to grasp because of the strong links to human perceptual abilities. A classroom demonstration of a loud sound concealing subsequent quieter sounds is useful.

Electronic hardware and software The final project, the construction and programming of the musical memory game, gave students a great deal of personal satisfaction. They began the day with an unpopulated printed circuit board, a handful of components and a lesson on soldering, and at the end of the day they took home a working electronic game to show off to friends and family. Beyond the project alone, students had a glimpse of the hardware and software that are “inside the box” for so many items they use every day. Student workbook and teacher solution guide A workbook was designed to help guide and focus student activity. The workbook contained the instructions to follow, worked examples, and spaces for student calculations and entries. Workbook excerpts from two lessons are provided in Figures 5 and 6. The Digital Music Math workbook is available upon request, as is the accompanying fully-annotated teacher’s guide, including solutions for all exercises.

4. REFLECTIONS The alternation between laboratory and classroom activities added variety that helped to maintain student attention. In addition, lessons were designed for high interest. Many lessons involved hands-on elements, such as tuning forks, electronic components, breadboards and multimeters. And, even though computers are really no more “hands on” than pencils, the e-learning activities based on the online piano and digital audio software created similar high attention levels among the students as did the manipulations of more concrete objects. Another, lesser, motivator was the completion of the workbook pages for each lesson.

Figure 5. Excerpt from Lesson 1.

Figure 6. Excerpt from Lesson 3. The technological tools allowed many STEM themes to be explored – math (scientific notation, ratios), pure science (tuning forks, sound), technology and engineering (spectrum, MP3 compression, programming, electronic circuits) – at a level suitable to Grade 9 and 10 high school students. Many of these themes are traditionally considered to be specialized and advanced, but immediate feedback through the use of technology made the concepts quite accessible, even to junior high school students with lower than average math facility. Access to concepts was further facilitated because numerical grading was not applied for this lesson series. Neither students nor teachers had to be concerned about whether everyone was learning at the same rate. Observation suggests that freeing students to explore and enjoy activities produced useful learning that was permitted to vary by student. The choice of music as a core theme was a good one for an Aboriginal classroom: The Canadian Council on Learning [8] reports that Aboriginal youth (37%) are more likely than all Canadian youth (27%) of a similar age to participate in art or music, with more Aboriginal girls than boys participating. One of the goals of the day-long field trip visit to Camosun College was to encourage students to visualize themselves as future college students. Their teacher confirmed that her students “got a glimmer that this was something they could do.”

5. STUDENT AND TEACHER FEEDBACK The students loved the Digital Music Math lesson series, especially the field trip to Camosun College and the building of the electronic game. Students said: “I really

had a lot fun,” “My favourite part was recording my voice on the computer,” “I liked learning how to solder,” “I’d do it again in a nanosecond!” Cora Oliver, the teacher, felt the students got a lot out of the lessons. She observed that students did well when they could see connections, and that interesting tidbits hooked student interest. In her own teaching, she strives to make math a hands-on activity because so many of her students are kinesthetic learners. Cora notes that her Grade 7 students exhibit on average a Grade 3 math level and if she were to use the lesson series again, she would be inclined to do so with higher level students and to extend the series to allow more time for repetition and review.

6. CONNECTIONS WITH RESEARCH The 2010 “Handbook for Educators of Aboriginal Students” [9] encourages: frequent interaction between students and faculty, cooperative, collaborative and social learning, active learning techniques, prompt and constructive feedback, learning tasks that respect cultural differences, high expectations, and diverse learning experiences. It also recommends a “focus on experiential learning rather than exclusive reliance on teacher-led discussions focusing on texts” [9, p. 20]. The Digital Music Math lessons align with many of these principles. Perso uses the phrase “inclusive pedagogy” when she recommends that “teachers and students should interact and negotiate meaning as equals, since this will result in students empowering themselves to succeed rather than waiting for and expecting teachers to ‘drip-feed’ knowledge in an effort to maintain control and authority” [10, p. 45]. Freedom to explore unique uses of the technological tools within the lessons promoted this kind of equality and helped to narrow the “power distance” between teacher and student in a culturally-responsive way. Perso points also to the importance of shared experiences of teachers and students in strengthening a “shared mental context” for learning. Interestingly, the students’ teacher reports that her students’ recollections of the field trip are particularly strong because their school bus became stuck in the snow during an unusual snowstorm in the region. Finally, the 2008 “Learning Indigenous Science from Place” report [11] suggests incorporating a balance of academic and fun activities. The report notes that presenting lifeless facts for rote learning turns students away from sciences, and that for Indigenous peoples rigorous mental learning is always balanced with fun, humour, and laughter.

7. FUTURE WORK In future iterations of the Digital Music Math project, greater attention can be given to cross-cultural issues. As Aikenhead points out, many students experience school science learning as “assimilation into a foreign culture,” and “the problem of alienation is more acute for Aboriginal students whose worldviews, identities, and mother tongues create an even wider cultural gap” [12, pp. 2-3]. To this end, a number of directions may be explored with the help of Aboriginal educators to attempt to align the Digital Music Math lessons more intelligently with research findings: • Aikenhead [12] describes the concept of “coming to

knowing” in participatory learning and its implications for power sharing in the classroom.

• Perso’s “integration of culture” [10, p. 41] inspires the possibility of integrating lesson elements that are culturally stronger, e.g. students might elect to program a drum sequence instead of song.

• Cajete advocates that teachers involved in Indigenous education “practice contexting information in culturally sensitive and holistic ways” [13, p.139], and proposes that storytelling practices will connect strongly with Aboriginal oral culture.

8. ACKNOWLEDGEMENTS

The author wishes to thank Cora Oliver, the LÁU,WELNEW Tribal School, Schneider Electric, Dianne Biin, Marla Weston, Ian Browning, and Camosun College for their support of this project, and to acknowledge the welcome she received in the traditional territories of the Tsartlip, Pauquachin, Tseycum and Tsawout peoples.

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