Desired results The main purpose of my teaching is to show to my students that mathematics can be seen and applied almost everywhere. Mathematics is not only an abstract language but it has real world applications and can be transformed into a common language and therefore mathematics is relevant to everyday life. I believe that my job is to uncover the mysteries of mathematics for my students as well as to help them develop mathematical competencies and consequently critical thinking skills. Mathematics is a trans-disciplinary field and can be applied in many different disciplines. According to Gardner & Mansilla in order to develop disciplinary competency, learners need to acquire four capacities; understand the purpose of disciplinary expertise, understand an essential knowledge base, understand inquiry methods and understand forms of communication characteristic to the discipline. Authors also suggest that teacher should help students to identify essential topics in the discipline. These topics are not only essential to the discipline but they also represent students’ interest within the discipline. My ImagineIT project includes Wonders of the World related to mathematics presentations which will be made by students. I would like my students to expand their interest in mathematics as well as their skills of explorations and research. During the process of preparation, presentation and/or further examination students will be able to find and unfold the mystery of mathematics. Another recommendation made by Gardner & Mansilla with regards to disciplinary competencies is to study fewer topics for longer periods of time and achieve deeper understanding in that smaller area of discipline. Therefore, students become experts in a specific area of study. In my classroom, students will be able to learn procedural mathematics along with real world applications of mathematical skills. It will be done through inquiry, investigation and exploration. I will try to demonstrate and teach my students different perspectives on certain topics. I will connect mathematics and mathematical skills with different subjects that students are learning and their real life situations. I will use the multimodality approach in teaching, studying and learning. I would like my students to gain an appreciation towards mathematics as a “queen” of all disciplines. As a result, I would like them to develop awareness and mindfulness of mathematics being around them everywhere. Lastly, authors Gardner & Mansilla advocate for developing performances of understanding. I believe that understanding a particular topic or discipline means applying knowledge from the discipline in the known and unknown situation(s). Students will apply basic and higher order thinking skills like knowledge, comprehension, analysis and synthesis. Moreover, students can be asked to create new problems or situation(s) that involve topic(s) just learned through application, analysis and evaluation of the topic and their own knowledge. In addition, creating new problems or situations for application of the particular skill will include forms of communication that are characteristic to mathematics. Therefore, students demonstrate full mathematical competency.
Performances of understanding
Performances of understanding are critical parts of teaching, studying and learning. Mindful use of formative and summative assessments help teachers to plan teaching topics or skills as well as re-teaching conceptually misunderstood skills. Particularly, formative assessment monitors students understanding so teachers, along with students are always aware of the strengths, weaknesses and misconceptions in the process of learning. In the intervening time, teachers can improve the effectiveness of instructionand/or address misunderstandings of the whole class or specific student. Understanding will be checked using several different modes. Each unit will have pre- and post- self-evaluations. I will post a chart on Google Classroom with major skills and topics covered in the unit. This chart will include four columns; the name of the skill, “do it” part, possible application and student self- reflection. We will revisit this chart weekly so that students will be able to monitor their progress. Traditional summative assessments will be given to students at the end of each unit. This summative assessment will take the form of performance tasks which incorporate basic skills understanding as well as application of these skills in real world situations. While teaching and assessing students’ understanding, I will pay close attention to four out of six facets of mature understanding developed and presented by Wiggins & McTighe in “Understanding by Design.” These four sides of viewing the concept(s) are: explain, interpret, apply and have self-knowledge. The first three of them are closely related to three basic questions: “What?”, “How?”, and “Why?.” I will ask these on a daily basis. For example, I will incorporate questioning and discussion regarding objectives of the lesson with a focus on how, why and where we apply specific mathematical skills or concepts. Having self-knowledge is a facet of mature understanding that I will try to develop with my students through self-evaluation charts. On a daily basis I will use traditional tools in checking for understanding like observation, exit slips, quizzes, guided and independent inquiry assignments, and hands on activities. At least once per unit I will apply assessment that involves technologically advanced practices. For instance, students, in pairs, will prepare presentations on Wonders of the World that incorporate mathematics and their own personal interest. Moreover, every unit will include either a project, mini-project or audio- visual, creative and artistic poster or video related to the mathematical content uncovered. Every once in a while I will use www.getkahoot.com to review certain skills or concepts. Gaming always engages and motivates students to be the best.
Learning experience and instruction
Context: I currently teach mathematics at Bogan Computer Technical High School on the South Side of Chicago. All of our students have chrome-books and we are one of the first CPS high schools with a 1:1 teaching approach through technology. Four years ago we started the school transformation process which includes changes in overall school culture as well as academic improvement. Our student body is racially, ethnically and academically diverse. For example, we have 50% African-American students and about 50% Hispanic. The majority of them come from low-income households. In addition, we have a large population of students with IEPs and many English language learners. Moreover, Bogan Computer Technical High School is authorized as an International Baccalaureate World School. Our unique program offers the IBO's renowned curriculum to all freshman and sophomore students with a 2 year Middle Years Programme and another 2 year Diploma Programme for those selected from within our neighborhood school for their dedication to their personal academic excellence and growth. My teaching assignment includes Advanced Algebra for juniors as well as IB Mathematical Study and Mathematical Ideas for seniors. All of my students are enrolled in my classrooms on www.thelearningodyssey.com and www.khanacademy.org. In addition, I use a smart board and Google Classroom, which serves as a means to upload all power points, assignments, activities and announcements. Students also turn in some of their assignments and projects on the Google Classroom. This coming school year I will meet my students daily for 45 minutes period.
Content: For the purpose of ImagineIT project I will concentrate on Advanced Algebra and Mathematical Ideas classes. The mathematical content of these classes involves real numbers system and operations within systems in different settings, solving equations with one variable, simplifying polynomials, applying polynomials, setting up and solving quadratic equations, linear and exponential functions, elements of finances and trigonometry as well as statistics including normal distribution. All topics include an understanding of basic skills along with their application in real world situations. Usually in my lessons I incorporate hands-on, inquiry type activities which use students’ prior knowledge. I would like my students to build up awareness and interest towards mathematics around them in everyday life. Moreover, I would like them to practice and become experts in explaining, interpreting and applying mathematical skills mindfully. I would like to increase excitement and students’ anticipation in their own learning. As far as the content knowledge is considered, I will make sure that knowledge acquired by my students is challenging and accessible.
Pedagogy: In my teaching I will use the TPACK (technology, pedagogy and content knowledge) model. Pedagogy is the art of teaching and assisting learners with different types of intelligences and studying or learning styles in the process of education. Pedagogy includes different types of teaching styles and instructional strategies. My pedagogical approach includes varieties of different teaching styles and instructional strategies. Sometimes, I will demonstrate and coach students in their learning process through practices and feedbacks given for correcting their misconceptions. On other occasions, when appropriate to the objective(s) of the lesson, I act more as a facilitator. It takes place when students are working with hands-on, inquiry type of activities. As the facilitator, I monitor students’ work, challenge them with questions and encourage students to ask questions. I believe that the teacher-facilitator model helps in developing critical and analytical thinking skills as well as a deeper understanding. In my classroom I will use varieties of pedagogical instructional strategies such as demonstration and explicit teaching which are teacher-centered approach along with modeling, individual tutoring, inquiry and think- pair- share strategies which build student- centered learning environments. In addition to utilizing individual practice for students, I will use pair and group collaboration as means of instruction.
Technology: Since Bogan High School is 1:1 chromebook school, all of my students will use computers on the daily basis. In addition, the Promethean Board will be used every day for classroom instruction and activities. Moreover, I will use videos, Desmos graphing application and/or TI-84 graphing calculators as tools necessary for further exploration, analysis, interpretation and application. Power points or Google Slides will be utilized for direct and indirect instruction. My students will complete homework and some other assignments on www.thelearningodyssey.com where every topic includes video presentations. Use of technology in my math classrooms will support me as a teacher in tracking individual student progress and in transforming my classroom from teacher-centered to student-centered. The ongoing monitoring and analysis of class progress provides flexibility in changes during the course. I will also use www.getkahoot which I consider to be a great site for review as well as for short term assessment. Besides all technology that I have been using so far, I will incorporate Google Drawing for creating posters or videos. Later on, students can share and present their work with other classmates, the school audience and community through Bogan Media Center. I want my students to see mathematics, to apply mathematics and to become creative, life-long learners of mathematics using technology.