1. Introduction

In everyday life, people use devices such as cell phones, iPods and digital cameras, which use audio and image processing technology. Although Ngoh and Jahangir[1] in an article titled “Is technology a curse or a blessing to our students of today”, it was clear that these technologies can be used in classroom applications to motivate students and make science relevant to their learning. Despite some minute issues revealed as the dark side of technology for students, it was still evident that these technologies offer entry to every student regardless of his/her ability, and they offer the student a means to achieve success at his/her level of education.

STEM, Science, Technology, Engineering and Mathematics, education has become a key topic of discussion and planning in the United States in recent years. With the ever increasing rate of innovation and discovery, it is vital that today's teachers are kept up to pace with the rapidly changing landscape of STEM fields. Ironically, the technologically dependent society of today is producing fewer scientific and technology careers. STEM is preparing students to be productive and responsible citizens, which is the basis of modern European education.

Jan Amos Komensky in the 16th century strongly believed that the basis of society should be an educated citizenry[19]. Several reports, such as “Rising Above the Gathering Storm,” emphasized that the scientific and technological building blocks critical to our economic leadership are eroding at a time when many other nations are gathering strength. This committee prepared four basic recommendations that focus on the human, financial, and knowledge capital necessary for US prosperity. One of the four recommendations focuses on actions in K–12 education (10,000 Teachers, 10 Million Minds). The report recommends strengthening the skills of teachers through training and education programs at summer institutes, in master’s programs, and in Advanced Placement (AP) and International Baccalaureate (IB) training programs [2]. Enrollment statistics indicate a decrease in the total number of students entering a STEM field of study. Current teaching methods and didactic-style classes are failing to attract, inspire and retain the next generation of teachers. Thus, it is imperative that a generation which is so dependent on modern technologies becomes able to understand, use and create ideas and projects with STEM technologies.

It is necessary to develop academic programs that will give teachers the knowledge and skills demanded by today’s K-12 education. STEM advances have drastically changed the landscape of K-12 education, thus increasing the demand for highly skilled teachers who have the knowledge to take full advantage of what the continually evolving STEM fields have to offer. Thus, as these fields evolve, K-12 teachers are increasingly required to update science, technology, engineering, and mathematics courses and programs. Hence, ensuring that the courses offered as part of secondary education are up-to-date with current and emerging trends in STEM areas, virtually guarantees success in terms of the number of students pursuing their careers in STEM fields.

A particular challenge is to provide subject matter content for K-12 teachers. Teachers need exposure to subject matter that allows both review of key concepts in their fields and expansion of their knowledge into new fields, in constructivist settings. In addition, they need to develop relationships with scientists to improve their general level of professionalism. The way that teachers present curriculum is largely dependent upon their understanding of and beliefs about how subject-matter should be taught[3-5]. When curriculum materials are designed to support teacher learning of new pedagogy and subject-matter, teachers are more likely to implement the curriculum with greater fidelity[6].

In 1999, Infinity Project[7, 8] innovators prepared engineering curricula for middle school, high school, and beginning college students by using audio and image processing techniques and technologies. The curricula and pedagogy developed through this project continue to help educators deliver maximum engineering exposure through hands-on engineering learning in today’s classrooms. Our developed course expands this project to the post-secondary level of both teacher preparation and in-service teacher training.

The principles of digital audio and image processing have applications in an amazing diversity of areas, from science and engineering (biomedical engineering, astronomy, video and wireless communications) to entertainment (music and video games). Digital audio and image processing education needs to be able to cater to a wide spectrum of people from different educational backgrounds. These fields draw from a great variety of academic disciplines, including mathematics, biology, acoustics, computer graphics, computer vision, optics, and computer science. It is essential to present these inter-disciplinary topics to middle school and high school teachers. These proposed multi-media experiences will teach pre- and in-service teachers the content and pedagogical tools with which to guide students to an understanding of these digital topics.

A particular challenge in a graduate program of secondary mathematics and science teacher education is to provide subject matter content on a graduate level that does not replicate undergraduate content. Teachers need exposure to subject matter that allows both review of key concepts in their fields and expansion of their knowledge into new fields, in constructivist settings.

Sanders[9] stated that the ideology of the field now called technology education has always been grounded in general education[10-17]. He explained that “…Interest in curricular connections with science, mathematics, and engineering dates to the 1870s, when Calvin Woodward—a mathematics professor—began employing manual training methods with mathematics and engineering students. The field’s mantra—“technological literacy for all”—clearly reflects its general education philosophy...” Therefore, integrative STEM education promotes learning through connections among science, technology, engineering, mathematics education and other general education subjects.

In this paper, we present a STEM course which is designed for pre-service and in-service mathematics, biology, chemistry, physics, general science, and earth science teachers in the University of Bridgeport. The course has an integrative STEM education approach. The evaluation and assessment of the course is also presented along with the feedback of the instructors and students.

2. Course Design and Content

This 3 credit, one semester course, STEM for Teacher Educators, offers base-level information on the theory and use of digital imaging and audio to improve the understanding of mathematical and science concepts such as arrays, matrices, sound production, how we hear the sound and how we see objects. The course is designed for the pre-service teachers in the School of Education. Participants will be engaged in up-to-date technical information, formulas, and simple programming algorithms, all designed to improve their level of understanding. This course helps its participants relate to math concepts through a “hands-on” multimedia approach using Mathwork’s MATLAB software through audio and visual applications. The goals of this course are:

● to teach basic knowledge on digital signal processing and technology with a creative interaction between music, speech, image and technology for STEM related courses such as mathematics, biology, and physics;

● to prepare instructional course materials for teachers to use in their classrooms.

This required course for the program will expose future teachers to new content materials. In addition, this “cross fertilization” will provide opportunities for participants to view subject matter in new perspectives. It will open avenues for new lesson development. EDMM-600D provides comprehensive professional development for teachers in two major engineering technologies which use many concepts from mathematics and science: digital audio and image processing.

The objectives or outcomes of the course:

● Develop knowledge and understanding about the practical and real world applications of audio (voice, speech, music) and image processing.

● Become familiar with audio and image processing hardware and software.

● Value and appreciate new technologies that enhance STEM learning.

● Be able to conduct hands-on activities and to teach the topics in the classroom.

● Be able to prepare instructional course materials for the classroom.

● Develop a range of skills relating to the presentation of course materials in a formal setting.

Course activities include both lectures and laboratory activities with hands-on computer experience. The evaluation of students’ performances has been done by midterm exam, homework assignments and project presentations.

Organization of the Course: Students are organized into groups of 2 or 3. Laboratory sessions are usually 2-3 hours. Sets of readings for each lab have to be read before class. Some readings are in text. Others will be handed out. Lecture will cover background material pertinent to lab, in these areas:

● The physiology of speech production

● The respiratory system

● The acoustics and acoustic analysis of speech

●Periodic and Aperiodic Signals, Logarithmic Operations

● Cardiovascular System and Heart Diseases

● The Ear and How we hear

● Logic, Truth Tables, and Sets

● Algorithms, Recursion Formulas, and Induction

● Linear Algebra

● The Eye and How we see

● Digital imaging

Team Project: Students choose one of the following possible projects.

Choose a topic (Logic, Truth Tables, and Sets, Algorithms, Recursion Formulas, and Induction, Periodic and Aperiodic Signals, Linear Algebra, The Ear and How we hear, The physiology of speech production, The respiratory system, The acoustics and acoustic analysis of speech, The Eye and How we see, Digital imaging) and develop

● A two-week unit designed to promote problem solving success in the area of your topic at a particular grade level.

or

● A unit illustrating the use of problem solving in this area over several grade levels.

3. Evaluation and Assessment

To assess and evaluate the students’ impressions of the new course, discussions were held with the students and a questionnaire was developed for distribution and collection at the end of the nine weeks. The questionnaire is given in Table 1. In composing the questionnaire, questions 4, 6, 7, and 12 are of special interest in assessing how the students value the new course. More than half of the students selected “Strongly Agree” or “Agree” when answering these questions. Of particular note were the responses to these questions, where 82% of the students agreed or were neutral. The instructors believe that these results demonstrate that the newly offered course does enhance the students’ understanding of the STEM concepts in this course. 100% of the students agreed that this course is very good or good as a learning experience.

One major concern of the instructors that was also expressed by the students was the prerequisite knowledge and skills required from students for this course. 36% of the students think that they have the prerequisite knowledge and skills for this course. They felt that if there was a physics instructor to have elaborated on the concepts and the calculations of the frequency, wavelength, with reference to waves and sound as well as on the concepts and calculations of the focal lengths, angles of reflection and refraction of light, they might have had the computations of the digital sound processing and digital imaging easier than what they experienced in the engineering laboratory.

Table 1. Results of EDMM-600D STEM for Teacher Educators Evaluation (%)

STEM is a common topic of conversation in many academic circles today and the integration of teaching methods is highly recommended. Always teaching subjects in isolation does not enable students to see clearly how one course is related to the other and how a course could be readily applied in real life situations.

When this course was designed, thought was given to topics that could easily demonstrate this concept of integration, relatedness and application of science, technology, engineering and mathematics in the society. It was for this reason that we chose sound or speech production, transfer of the sound waves to be heard and the acoustics involved and also how light and its characteristics made it possible for objects to be seen.

For biology, the instructor involved had to start with the respiratory system with emphasis on the larynx and the vocal cords. A clear description was made of how the vocal cords, the tongue and the lips all functioned in the production of sound. This was followed by a lesson on how the structure of the ear was adapted to be able to transfer the vibrations through the ear to the brain for the noise, music to be heard. The waves gathered by the pinnae into the auditory canal hit the tympanic membrane whose vibrations were transmitted by the ear ossicles to the oval window into the inner ear where sensory cells in the cochlear started off an electric stimulus through the auditory or cochlear nerve to the brain which interpreted the particular sound. Frequency, amplitude, pitch and wavelength were explained in such a way that students could easily understand when the technology/ engineering instructor would be calculating the wavelengths, frequencies and analyzing the acoustics of the speech.

Similarly, the structure of the eye was discussed for the students to understand how the reflection of light rays on an object made it possible for the refraction of light by the cornea, lens and the aqueous and vitreous humors helped formed the inverted image on the retina. The sensitive photoreceptors pick up the stimulus and send out the electrical impulses through the optic nerve to the brain which decodes the information for one to see the object in its up-right perspective. This principle is demonstrated by comparing the function of the camera with the human eye. When the students grasp this process of accommodation, they are well prepared to put this into practice with the math and engineering instructors calculating the object distance, focal length, the refractive index of the lens and the practical digital imaging concept.

The science part of the course was accepted without hesitation by this cohort of students because a good number of them had a solid base in human physiology. The real challenge and excitement came as the students saw these seemingly obvious topics approached from a practical angle as the engineering instructor simply transformed those concepts of wave production into sound production and hearing. Similarly, the reflection, refraction and transmission of light rays brought about digital imaging and seeing. Students realized practically how the convex and concave lenses were used to correct myopia, hypermetropia as well as astigmatism and diplopia.

Our original plan was to explain rather general mathematical principles of logic, algorithms and recursion formulas used in computer engineering, and then illustrate these principles in light of specific content materials in the course. Our first meeting concentrated on truth tables, basic principles in Boolean algebra and elementary circuit design, with specific problems involving simple series and parallel circuits. For some of the students, the material was a review, others found it a bit challenging.

While all had backgrounds in various sciences their knowledge of mathematics was very uneven. For example, those students who had degrees in physics, computer science, electrical engineering were comfortable with the mathematics we introduced, while those with degrees in biology, earth science, and to some extent chemistry, frequently had not studied much mathematics at the undergraduate level. They did not find the material particularly easy to grasp. Nevertheless, student feedback from the session was good. They had learned new ideas and were positive about the experience.

A much clearer picture of students’ understanding came during the next lab period. We realized that we had vastly overestimated their understanding of some basic mathematics. During this session problems arose with calculations involving logarithms. Many of the students were completely confused. They did not understand the most fundamental properties of logarithms; in fact, a number of them could not even give a specific example of a logarithm. This situation required us to face two problems.

● The first dealt with our long range goals: How to give students the basic mathematical background needed to ensure success in the course?

● The second was more immediate: What mathematics must we cover with students to ensure they would be prepared to complete the present course?

We decided that before we offer this course again, we would have to consult with each other, before the start of the course, about the exact mathematics that students needed to understand the engineering and computer science they would cover. We had to be careful to over-reach our goals. For example, if students needed to know information about linear functions we would not start talking about matrices, operations with matrices, inverse operations and matrix solutions of systems of equation. Rather, we would be sure that a student understood carefully the slope-intercept form of the equation of a line, and how to solve two equations with two unknowns by various methods.

With this new insight into students’ backgrounds we decided that the next “mathematics” class would concentrate on basic trigonometric functions. To the surprise of many in the class, we introduced trigonometric functions as circular and the corresponding reciprocal functions. Understanding that the basic three trigonometric functions, were values that could be read off the unit circle, allowed for a simple, yet rigorous development of trigonometry. The graphs of the trigonometric functions followed immediately. It was these graphs that formed the basis of the computer analysis of sound and light.

This experience underscored the constructivist nature of our work as teachers. We needed to exchange ideas with students about how they were constructing or not constructing knowledge. This dialogue, this exchange of ideas, then allowed us to construct course materials which students found meaningful.

Engineering instructor is responsible for connecting learning in mathematics and biology, which are taught by mathematics and science instructors, to appropriate real-world concepts such as audio and image processing technologies. The instructors think that the present and future K-12 Mathematics and Science teachers need to teach their curricula by an interdisciplinary approach. George and Thomaskutty[18] stated that “...most of the Mathematics classrooms are boring, especially, in the school level. Students either hate Mathematics, or fear it. The blame for this plight is partly to the teachers and the rest to the curriculum. Students get no interest in studying this subject, because neither the teacher, nor the syllabus points out the practical use of the prescribed portions. Here comes the need of coining Mathematics with other disciplines. There should be an interdisciplinary approach in teaching Mathematics...”

Mathematics is a common language of many disciplines and teachers should know mathematical concepts used in those disciplines so that they can teach their students how to connect their mathematical learning to appropriate real-world contexts. Although there is a belief that Biology is free from mathematics, Biology needs mathematics in a great amount. Engineering instructor presents computer/ programming based activities by combining the biology concepts --respiratory system, voice production, the ear and how we hear—with audio processing technologies and --the eye and how we see, vision-- with image processing technologies. Several challenges have been face during the lectures. One of them is the weak mathematical background of the students. Secondly, some of the students believe that applying this interdisciplinary approach in their classroom will be very difficult. This misconception blocks their creativity.

We have asked four open ended questions to our students about STEM education in USA. The students’ answers show that they are very interested in integrating STEM in their teaching however they are not sure how to do it. Some of the students’ answers are given below.

Question #1: In your opinion, what is the importance of STEM education in U.S.?

(Biology teacher, Female, Age 26) “...I think it is an interesting approach to teaching these courses. I am sure if properly implemented it would greatly benefit students...”

(Biology teacher, Female) “STEM education is extremely important for students, as well as for educators in teacher preparation programs. It helps to give students a more well-rounded education, and makes each of the subjects in STEM more relatable. With the integration of science, technology, engineering, and mathematics, students can see each of those subjects clearly in the world around them, bringing the content to life and making it of use to students in years to come. It stresses the application of the content, which is missing in many educational programs. From the point of view of teachers, STEM education better prepares us to educate our students in the most comprehensive manner possible.”

(General Science/Master’s in Education teacher, Male) “To compete with students globally universities need to integrate and emphasize the disciplines of science, technology, engineering and math.”

(Biology teacher, Female) “STEM education is extremely important for students, as well as for educators in teacher preparation programs. It helps to give students a more well-rounded education, and makes each of the subjects in STEM more relatable. With the integration of science, technology, engineering, and mathematics, students can see each of those subjects clearly in the world around them, bringing the content to life and making it of use to students in years to come. It stresses the application of the content, which is missing in many educational programs. From the point of view of teachers, STEM education better prepares us to educate our students in the most comprehensive manner possible.”

Question #2: In your opinion, what are the most important challenges facing STEM education in the U.S.?

(Biology teacher, Female, Age 26) “One of the biggest challenges facing STEM education today is a lack of content knowledge. For example, a science teacher may not have the necessary background to fully integrate mathematics, engineering, and technology into his/her curriculum, and vice versa. In addition, a lack of technological resources in some schools may hinder STEM education.”

(Biology teacher, Female) “One of the biggest challenges facing STEM education today is a lack of content knowledge. For example, a science teacher may not have the necessary background to fully integrate mathematics, engineering, and technology into his/her curriculum, and vice versa. In addition, a lack of technological resources in some schools may hinder STEM education.”

(General Science/Master’s in Education teacher, Male) “Most American students seem adverse to the sciences.  Our culture deems science professionals as geeks or nerds.  We need to make science COOL!!”

(General Science Education teacher, Female, Age 32) “I think the biggest challenge facing STEM education is funding, especially with the technology piece. I know that Professor Barkana said that there was a school that got a grant for the program we are using in our class but some schools are not this lucky. I think we need to put more emphasis on STEM education so we can get more funding sources for schools.”

(Biology teacher, Female) “One of the biggest challenges facing STEM education today is a lack of content knowledge. For example, a science teacher may not have the necessary background to fully integrate mathematics, engineering, and technology into his/her curriculum, and vice versa. In addition, a lack of technological resources in some schools may hinder STEM education.”

Question #3: Are you interested in integration STEM in your teaching?

(Biology teacher, Female, Age 26) “I am interested in integrating STEM into my teaching, but am unsure of how to go about it. I know that my students would benefit from it, and would receive a more comprehensive science education as a result, but I do not know where to begin.”

(Biology teacher, Female) “I am interested in integrating STEM into my teaching, but am unsure of how to go about it. I know that my students would benefit from it, and would receive a more comprehensive science education as a result, but I do not know where to begin.”

(General Science/Master’s in Education teacher, Male) “Of course, being a general science teacher it will be essential to integrate all four disciplines.”

Q4. Do you believe that this course will help you integrating STEM in your teaching? Why?

(Biology teacher, female, Age 26) “I do believe that this course will help me to integrate STEM into my teaching. As a Biology teacher, the content we have explored is already applicable to my curriculum. However, my only hesitation is that I will be unable to do it on my own due to a lack of expertise in mathematics and engineering. We have been exploring waves and their link to biology through the anatomy of the human ear. However, when I am exploring other areas of my curriculum, I am not sure how to integrate STEM.”

(Biology teacher) “I do believe that this course will help me to integrate STEM into my teaching. As a Biology teacher, the content we have explored is already applicable to my curriculum. However, my only hesitation is that I will be unable to do it on my own due to a lack of expertise in mathematics and engineering. We have been exploring waves and their link to biology through the anatomy of the human ear. However, when I am exploring other areas of my curriculum, I am not sure how to integrate STEM.”

(General Science/Master’s in Education teacher, Male) “I believe this course is an overstatement of the obvious, but it will look good on my resume.”

(General Science Education teacher, Female, Age 32) “This class has already got me thinking of how I can use STEM in my teaching. At my school I have heard the science teachers taking about stem in their classes and I hope to do the same. I think it can be use in earth science as Professor Barkana showed is with earthquakes. I think it can also be used in life science. Any of the functions and systems of the body can be linked to STEM as Professor Ngoh has shown us. Thinking out sound has made me think about using STEM to look at how we move or how the heart works, or any other function of the body.”

(Biology teacher, Female) “I do believe that this course will help me to integrate STEM into my teaching. As a Biology teacher, the content we have explored is already applicable to my curriculum. However, my only hesitation is that I will be unable to do it on my own due to a lack of expertise in mathematics and engineering. We have been exploring waves and their link to biology through the anatomy of the human ear. However, when I am exploring other areas of my curriculum, I am not sure how to integrate STEM.”

4. Conclusions

Improving teachers’ teaching quality is the most important investment that the higher education schools can make to prepare today’s students for college and career success. In developing a new STEM course, several issues needed to be addressed. First, the students with varying backgrounds as biology, earth sciences, and mathematics majors must be able to understand basic mathematical concepts in order to learn advanced STEM concepts. All of the students revealed or admitted that that they did not have a strong background in math and need recalls for performing basic numeric operations such as the elementary exponential, logarithm, and trigonometric functions. This issue has become a serious drawback, especially in MATLAB applications. A second issue is how to address the time commitment of the students. The students require more time for the MATLAB applications since they do not have a prior knowledge of programming. A change in the curriculum and credit-hours can be made, but this issue remains to be resolved by the authors. The instructors have emphasized cooperation and teamwork, and the students always are reminded to work on their communications skills with their team members. We hope that continues improvement of this course will push whom they need for integrating science, technology, engineering, and mathematics in our school. This will further highlight the relationships and the applications of the knowledge of these subjects into the society today.

ACKNOWLEDGEMENTS

Authors thank the students of EDMM600D STEM for Teacher Educators course for their valuable feedback.