Inquiry 1 Presentation

Hi everyone! Here is the link to our Inquiry 1 presentation. Thank you for listening!

Annotated Bibliography: Articles from self-research

I have compiled a list of articles for my annotated bibliography. All these articles are researched and selected by myself. Jacob, my project partner, has his own research that we will combine together for our presentation.

1.

Akpan, J. P., & Beard, L. A. (2014). Assistive Techology and Math Education. Universal Journal of Education Research, 2(3), 219-222.

The article describes various assistive technological devices as a math tool to help teachers in delivering instructions and to support students with varying learning needs and skills. This is important for our inquiry project because in any online learning environment, just like in traditional classrooms, those who are either struggling, gifted, ELL, or students with disabilities should feel included and accommodated in online math instructions.

2.

Clark, A. K., & Whetstone, P. (2014). The Impact of an Online Tutoring Program on Mathematics Achievement. The Journal of Educational Research, 107(6), 462-466.

The article is important for our inquiry project because it builds on the idea of online learning and what it means to both students and teachers. The research focuses on Math Whizz online tutoring platform that provides insights on the appropriate instructional methods for teachers when integrating it into the classroom. The research also shows how this online learning platform improves students’ attitudes, thinking, and problem-solving skills.

3.

Crawford, L. (2013). Effect of an Online Mathematics Curriclum for English Language Learners. Computers in the Schools, 30(3), 248-270.

The ability to learn mathematics instructional language while learning a new social language can be especially difficult for ELL students in K-12. This article is important for educators as it demonstrates that computer-based, online math classes are effective learning tools for ELL students, as long as it is appropriately designed with their needs in mind. The study focuses around middle school ELL students of Hispanic origin; it explains the importance of multi-modal learning for students and what teachers can do to encourage this type of learning in a virtual math classroom.

4.

Cross, T., & Palese, K. (2015). Increasing Learning: Classroom Assessment Techniques in the Online Classroom. The American Journal of Distance Education, 29(2), 98-108.

In this article a study done by Cross and Palese intends to discuss the importance of assessing students in online math classrooms, and which method of assessment, either formative or summative, is most effective for students’ math learning process. This is important for our inquiry project because from a teaching perspective, being able to assess students in an online setting is crucial for teachers to understand students’ learning progress, but to must also allow students to self-evaluate and reflect on their own learning.

5.

Edwards, C. M., Rule, A. C., & Boody, R. M. (2013). Comparison of Face-to-Face and Online Mathematics Learning of Sixth Graders. Jl. of Computers in Mathematics and Science Teaching, 32(1), 25-47.

The article compares the traditional face-to-face math learning with online math learning setting for Grade 6 students. This is useful for our project because it looks at how middle school students respond and learn in an online environment, and the advantages, limitations and recommendations associated with online learning that teachers like us should look for.

6.

Kim, C., Park, S., & Cozart, J. (2014). Affective and motivational factors of learning in online mathematics courses. British Journal of Educational Technology, 45(1), 171-185.

The article is important for our inquiry project because it investigates the several possible factors that help students excel in online math courses. The research focuses on why some students excel in online learning environment than others, and the key factors are due to emotional, motivational, and cognitive processes in K-12 students’ learning, in which teachers should consider.

7.

Serianni, B. A., & Coy, K. (2014). Doing the Math: Supporting Students with Disabilities in Online Courses. TEACHING Exceptional Children, 46(5), 102-109.

The article is important for the inquiry project because it provides a framework of practical ideas and factors on how parents and teachers can successfully guide younger students with disabilities in virtual math classrooms.

Exit slip: Longsword math activity!

I really enjoyed this activity in class and I cannot wait to share that with my friends! What I like about the longsword activity is that we individually were given coffee stir sticks to work with, on a small level; combined with the picture given on the board, we were able to work with a partner or by ourselves to create beautiful shapes and sizes out of these ordinary tools. I also worked on my own to create other artwork that is math-related too. Once I did that, I started to brainstorm other shapes that I could build, and I thought about where I see them in real life, or how these shapes can be used in real life. It is from my everyday life did I draw inspiration from, and I think students in high school and even elementary school would equally enjoy building something with their hands. This can also be a rewarding experience for the students, where they can learn math and create math out of ordinary objects. Doing this can also give students the possibilities of constructing other math shapes out of something we see and use every day. In a way, this activity reminds me of the EDCP342A math/art project where we use various resources from our every day lives.

The dance was enjoyable to learn as well. I find it much easier to learn something from doing and acting. I think this activity would be a great way for students to use actions to construct mathematically-created shapes. To let them "be and build the math", for the lack of better words, is a good learning technique that would definitely be a memorable experience for students in that they won't forget what they learned when they leave the classroom!

Entry slip: 1-Sentence Description of 3 Articles

Objective of this inquiry project with my partner, Jacob Brunner:

We will focus on online math learning for students in both elementary and secondary schools. We will also explore the possible effective math online learning tools that support students with differing learning abilities, such as students with special needs, ELL learners, and gifted students.

Article 1:

Akpan, J. P., & Beard, L. A. (2014). Assistive Techology and Math Education. Universal Journal of Education Research, 2(3), 219-222.

The article describes various assistive technological devices as a math tool to help teachers in delivering instructions and to support all students with varying learning needs and skills as listed in the objective.

Article 2:

Kim, C., Park, S., & Cozart, J. (2014). Affective and motivational factors of learning in online mathematics courses. British Journal of Educational Technology, 45(1), 171-185.

The article investigates the factors that help students excel in online math courses, and it reports that online math courses are more successful than others due to the emotional and motivational aspect of learning in K-12 students.

Article 3:

Serianni, B. A., & Coy, K. (2014). Doing the Math: Supporting Students with Disabilities in Online Courses. TEACHING Exceptional Children, 46(5), 102-109.

The article provides a framework of practical ideas and factors for parents and teachers to successfully guide younger students with disabilities in virtual math classrooms.

Entrance slip: Refocusing Our Efforts

From reading this article by John Sarte and Sherri Hughes, my "student bird" thought was that assigning percentages or letter grades may mean that I have to do extra well and put extra effort in achieving high percentages or letter grades. To me, as a student, these grades indicate a successful completion in passing a course or judging on how well or poorly I have done. However, it may not necessarily indicate an interest in the course that I am being assessed or marked on. It just simply means that I did the work, passed the course, and now moving on to something else. In some cases, a student with a poor grade does not mean that he/she is not interested in the course materials. Similarly, a high grade does not necessarily mean that the student is interested in the course. As often is happened to me when I was a student in secondary and post-secondary schools.

As a "teacher bird", the percentages and letter grades tell me how well a student is doing in the class. I assume that higher the grades, the higher level of understanding and/or competency a student has. I would also assume a higher interest in the course because the student is excelling. However, as argued above when I was a student, what is on the surface may not be accurately perceived. As a teacher, I believe that grades should be arrived by how well the students are doing throughout the course of learning and teaching a particular subject or topic even. Assessing their understanding on a certain day, as in most cases (i.e. unit test or exams on a certain day of the week) may not be an accurate prediction that determines the ultimate result of students' learning, as many factors can affect students' learning and thinking abilities. I believe this is the negative aspect of giving grades. The positive aspect of giving grade, however, is for teachers to keep track of where students are standing academically in a grade and subject. It also informs teachers what and how they should do to help students achieve. That being said, teachers should not disregard the stronger students just because they are excelling more than the weaker students. Teachers should give equal opportunities and promote interest among all students.


An unintended side effect of grading is that students may get pressured into thinking that just because they are being graded lower than their peers, they may feel not as motivated to learning concepts or push themselves to work harder. They may also not feel interested in the course because the grades are lower than wished or expected. This discouragement could affect students' competency and thinking abilities. That being said, grades and marks could also form a social relation in that they students can keep track of their skills and levels among their peers. It tells them which area they need help or improve, and which area they are really good at that they can help others. Motivating each other with their peers are important in establishing social relations in classrooms and higher institutions.


It may be quite difficult to not give grades to students who are learning math and/or physics, but I think that as long as teachers and the students themselves know where they stand academically, and which area they need improvement or excelling, then grades may not be very important. It is a good habit, in my opinion, if the students develop some sort of work ethics so that they are encouraged to learn and try new things without having an authority figure telling them what to do. Once they internalize this interest for learning and that they are always pushing themselves for higher knowledge, grades should not matter.

I can compare this analogy to my co-op placements at various companies during my undergraduate work terms. I had a few co-op placements in the past where it was not necessary for co-op advisors to report the school on our mid-term performances (evaluating and marking how well we do on the job). Even though my co-op advisors did not visit us during our co-op terms, that did not stop me from doing well on the job. Often times, weekly or bi-weekly, my managers would speak to me and my team (individually or as a group) on our performances, and what we should do more or less of, and what we should focus on. Their "mini-evaluations" just by speaking to us gave me a professional outlook on work that lasted me for a long time - still do even now. Their comments and suggestions have pushed me to work harder and better on the job, regardless of which profession I will be pursuing in the future. In this case, I have developed good working ethics from my employers and my team of co-workers, which I am very thankful for. In the teaching aspect, I think that if teachers can set students good examples for the students to model after, then that skill set and attitudes are definitely worth having and are more important than grades.

Exist Slip: Research for Inquiry I Project

The topic that Jacob and I will be doing is revised slightly.

Our topic now focuses on online learning in students on the subject of mathematics, with additional focus of online learning in students with special needs. Essentially, we will look at the impact of online learning in math subject on various students - students who do not have special needs and students who do.

Inquiry Project Ideas

For my inquiry project for this class, there are two main topics that I want to look at, but of course I will have to pick one to analyze.

One particular topic of interest is the idea of a flipped classroom, and the theme of online learning. I am very interested in looking from the perspective of a flipped classroom because I have designed eLearning materials, in collaboration with professors and using software to facilitate in the learning of college students. I wonder how well high school or middle school students take in concepts from the online platform. However, the concept of a flipped classroom is different than having an instructor teach through an online platform in that students are expected to learn the materials and teach themselves online first, then coming to class, knowing the materials, and apply the knowledge in the real world. So I want to examine how effective this flipped classroom and online learning is for younger students.

Another topic of interest that I may examine is poetry and mathematics. Because I have taken tons of English courses that examine poetry - particularly forms, counting metrics, finding rhythms in stanzas, etc. - these patterns in the body of the poetry amazingly tie with mathematics. Poetry has its beautiful poetic forms and so does mathematics. Poetry is an art, and we were discussing how mathematics can be used to create meaningful art, such as poetry itself. I would like to examine this topic further.

Entry Slip: Article on "Ancestral Genres of Mathematical Graphs"

Susan, the article you wrote is certainly interesting to read and analyze. I have also thought about why right and up indicate positivism, and left and down indicate negativism. I've encountered this especially in units on graphing and sketching equations, such as a linear equation, parabola, and many other shapes. I understand that it is common to think that right and up is associated with positive because of the points you touch on in your article. I also believe that our culture and norm definitely have something to do with the naming conventions. I mean, after all, they are supposed to be "arbitrary assignments" (15). And interestingly enough, because culture is different across the world, for instance, the North American (Western) culture may be different than South American culture, but the universality on the existence of culture leads to the same conclusion in the "genre" of mathematics. In Asia, specifically China, Chinese also associate any numbers left of 0 to be negative, and any numbers right of 0 to be positive. Again, this name convention is universal across culture.

One area that made me think more about this convention of this "hidden", "arbitrary" assignment is the CAST rule. I learned the CAST rule in high school in units on trigonometry. The CAST rule, which stands for Cosine, All, Sine, Tan, is a grid that is divided into four (4) quadrants where it tells us what trigonometric ratio (cosine, sin, tangent, or all) is always positive in a said quadrant. Counting using the CAST rule starts in a counter clock-wise fashion. First quadrant is positive in A, second quadrant is positive for S, third quadrant is positive for T, and the fourth is positive for C.

This is an image that was taken from Google to demonstrate the idea of the CAST rule. Applying the CAST rule to calculate the exact values (in fractions) of trigonometric ratios may not apply to the "right/up" positive and "left/down" negative convention, since trigonometry of a certain function follows a smooth, continuous curve that repeats itself depending on the degrees it has. The +/- sign of a trig function really depends on the angle or the degree that it is given. The angle and the exact position can be shown on a 360-degrees circle. So, I'm not really sure if the conventional naming of positive/negative still applies in this case because trigonometry deals with continuous functions, not something that is binary, which has front and back, up and down, or left and right.

While reading your article, I was also fascinated by the image included in your article of Albrecht's (1471-1528) portrayal of an artist is drawing a model through a frame using a grid system. This got me interested by the artist's sketch of human facial symmetry and the many patterns that exist in nature. I'm particularly interested in facial symmetry because body measurement, especially as seen on faces, influences judgement and qualities (e.g. positive and negative social cues) of an individual. The aesthetics behind facial symmetry in certain culture has a deeper meaning than just the appearance of the face. For instance, Chinese physiognomy used to be so popular that Chinese people assessed a person's character and personality just purely on their facial constructions. The connections between mathematics of symmetry in the human body with the culture aspect that is influenced by it is astounding and can be quite controversial. However, complex mathematics cases such as the trigonometry functions may show otherwise.

Exit Slip: Take Away From Personal Phenomenological Experiences

From our personal phenomenological experiences, the takeaway of this, in my opinion, is the concept of "human" aspect of teaching - and just human aspect of social interaction between each other. Interacting with others is all very important for us all, and that including everyone (accommodating and adapting to students' learning needs). We also talked about authority, and how students are more intimidated by teachers with high authority because they may be less likely to ask questions and seek help. So, if a teacher is more "human" and not just a "robot" (or a scary authority figure), students may be more inclined to seek help and be more interested in the topics that they teach. In all, the concept of being sociable and human-ly to others (i.e. respecting and adapting to students' needs) are very important!

Personal Experience in a Formal/Informal setting

When I was around 6 or 7 years old, my parents signed me up for swim lesson, to much of my surprise. I was never a good swimmer, and I didn't like the idea of being inside water (I was always afraid of swimming in deep ends due to my fear of drowning). I can't remember much about the first day of swim lesson, but I did remember my learning process in between.

First of all, I really did not like the smell of swimming pools, or anywhere beyond that matter. And second of all, the pool was used not for recreational purposes, so there weren't too many people swimming for leisure. I know that if I drown, they won't be in time to catch me or I won't have anyone to hang on to. As you can probably imagine, to get me actually inside the water was tough. However, as time goes by, I got used to this fear. My swimming instructor, a young woman, was very calm and patient with me. It's as if she understood my fear of water and seems to be okay with me acting this way. As well, I wasn't the only one who is afraid of swimming in deep ends. Knowing that I wasn't alone in this made me feel more comfortable. My instructor was also with me, side by side, knowing that she will catch me if I did drown. She was my lifeguard. Slowly, as time goes by, I gained confidence and independence, knowing fully well that I can swim on my own.

At the last day of my swimming lessons, I remember there was a big swim race, where beginners like me race across lanes. I remember I was competing with this other girl around my age, and I couldn't believe that I got to the end before she did! It was a rewarding feeling, and both my parents and the instructor were very proud of me.

Entry Slip: 3 Quotes from Max van Manen's Article

Quote 1:


"If teaching is indeed caring profession then the caring involves helping, encouraging, admonishing, praising, prodding, and worrying about individual students and classes."


I think caring for students plays a huge role in students - not only in their learning, but also in how they socialize and interact with other students and teachers. As I can recall, even now as a BEd student, it really motivates me to learn something new because my teacher really cares about me and how I can possibly achieve greater things in life. If I see a teacher is trying to really get to know us, the students, and not just being a bossy teacher (a "robot") who just constantly dictate us on what to do all the time, it really motivates me, in turn, to get to know the teacher and the subject (content/materials) she or he is teaching. The "human" aspect of teaching is very important here. As long as students know that teachers are always there for them, to help and to encourage (even with a bit of constructive criticism), students do experience "positive experiences".


Quote 2:


"Recognition is inextricably intertwined with selfhood and personal identity. And self-identity is the realization of the tension between being of self and the becoming of self, between who we are and who and what we might become."


I recently read a book called "The True Diary of A Part-Time Indian" by Sherman Alexie. It is about a young Native American adolescent from the Spokane Reservation. The struggles this young boy goes through, especially in an educational institution (such as his school), is just as troublesome and complicated as things that are happening in his home (and his social life). The young boy has big dreams - of making it big, whether it is in his personal life or in his academic/social life. Because he knew that attending a school on the Reservation is not going to get him anywhere, and his Reservation teacher knew that too, so his teacher told him to aim for his dream by leaving this school. It's a big step and a big commitment to leave this place and go somewhere different, foreign, new. However, the book ends with him "making it big" at his new school where he actually mattered to everyone - his classmates and his teachers. He made it big while being on the school's basketball team; he made it big and excelled in class by doing the things he likes. He was given the opportunity to be himself, to not be afraid to speak his mind. The message of "self identity" and "becoming of self" is so important here.


Quote 3:

"What distinguishes practice from theory is not that practice applies thought or concepts technically to some real thing in the world upon which it acts. Rather, the phenomenology of practice involves a different way of knowing the world. [...] Theory "thinks" the world, practice "grasps" the world."


This quote speaks volume! I am a strong believer in applying theories and what we learned into real life. Although not every student understands theory to their best abilities, some may struggle with theories - like me (it takes me longer to understand theory, but less time to apply the theories) - while others capture theories quickly. I think it is a good idea for students to understand theories behind certain concepts as they can apply the theory to many applicable areas. Theories are fundamental basis for many things that we study in life. Incorporating that into the class and be able to transition between theory and practice is important in the classroom. This engages students with critical thinking and learning skills, the teachers can gain new perspectives on how students think and reason, and parents may be surprised by their child's ability to comprehend advanced things - this maturation in their cognitive development may increase.

Exit slip: Jo Boaler, Beautiful Maths

The video by Jo Boaler is really interesting! She touches on a lot of points on methods to educate students. She proved this by examining and experimenting one-dimensional math vs. the multi-dimensional math. From my experience as a high school student, I think it was a mix of one- and multi-dimensional learning from my teachers. I think as our society is changing and growing rapidly, especially in education field, teachers are trying to find ways to engage with students and have students engage with the subject being taught. I do like the collaboration and debate on subject areas, even now at university, it helps me (and maybe others) to get my brain moving. It's this type of maturation in our critical thinking that helps us with our understanding.

Boaler has also touched on the concept of a growth mindset and a fixed mindset. I completely agree with this thinking. Actually, even now during my undergraduate studies, there are hard math courses that are particularly challenging to me, but for others, it's a piece of cake! I can see by their way of reasoning on questions and their way of grasping a concept so quickly, whereas it would take me a while to finally understand them. Maybe it's because of this sense of "hidden competition" in understanding concepts and finishing our assignments that makes me think I'm just not cut out for this course. I had a fixed mindset back then, and it is not a good thing. It really limited me in being involved with the homework questions (as I would often times delay doing questions or studying for the course), and it made me fear the course even more, knowing that others are way ahead of me.

However, over time, I developed a growth mindset, as discussed by Boaler. With a growth mindset, I would know that I may not be alone in having trouble understanding certain areas, and that it is better to seek help early than later. I had also worked in groups to study for tests or working on assignments together (we would discuss openly about various units). Sometimes, I may think that I really understood things in the course, but upon debating with others, I realized that there was a whole new spectrum of things that I did not know or may not have covered during my studying time! This kind of method of learning really helped me, as well as my group, to gain a better insight on the course.

Entry Slip: On Becoming a Reflective Teacher

1.

"On Becoming a Reflective Teacher" is certainly an interesting article that feels more personal than as if I'm reading from a textbook that is filled with facts. The article speaks to me because I feel that teaching is a profession that may be changing in the ways teachers teach over time. Although the fundamental goal of teaching remains fixed: to educate students and to provide support in their learning, but the ways to achieve this goal can vary from teacher to teacher, and in different academic settings. In fact, just by looking at our debate on relational vs. instrumental ways of learning among students, I can clearly see how teacher candidates like us are distinguished. As Grant and Zeichner first stated in the article, "teachers differ substantially according to their goals and priorities [...] that they employ." (103)

An insight that made me question myself as a teacher candidate is being mindful of the "teaching procedures and strategies" (106). It does seem easy to do, as teachers should be open-minded of students' learning, and it helps the teacher to be engaged with and care for his or her students. However, I'm just unsure when and how, if such opportunity rise, should I - a teacher candidate - should address issues that may be hidden from the "standard" or the teaching "tradition". Perhaps I don't have enough experience as a teacher in a classroom setting, and I can't say if it is ideal to question the standard way of teaching in the curriculum... Of course, one way of being open-minded is to be flexible and adapt to student learning styles.

As seen in the example in the article, I can't say if boys are registering in more science/math/technology classes than girls now since all genders are assigned the same class, so they are receiving equal amount of knowledge in those subject areas. In fact, we are now pushing more young people towards these field of study with the growing resources to fulfill our curiosity!

2.

The article's concept on being a reflective teacher has definitely made me open my eyes on ways to improve myself and what I do passionately. The fact that we are all in this teaching program together, a professional development program, makes us reflect on ourselves, our experiences, and our attitudes towards professionalism. As I was reading through this article, my mind was constantly thinking back of my examples when I was a student teacher and a tutor, and in what ways I could have done better or improved. For example, when I was volunteering as a teacher's assistant years back, I had always stuck to responsibilities and did things that were told by my homeroom teacher. I had also assumed that every student is paying attention and being engaged in the lessons. However, I should have been more open-minded to everyone in the class, and not just making assumptions. I needed to take active control as a student teacher by putting my mind and heart out there. As Grant and Zeichner points out, the reflective teacher is "dedicated and committed to teaching all students, not just certain students." (107)

Exit Slip 1 - Sept 17

Today in my EDUC450B workshop, we watched two videos on Frank McCourt. Both interview videos are really inspirational and provided a lot on teaching strategies. One of the most important take away from his interview is that we must "teach the students, not the subject". I cannot agree more on that. In his interview, he said that he taught at vocational schools, and one subject he taught was E.S.L. Of course, learning a new language is difficult, especially for adolescents. And the fact that teachers should accommodate student's learning is a great way to motivate and engage them. McCourt also explains the importance of getting to know the students better and knowing where they are coming from. Drawing from my personal experience, I immigrated to Canada from China when I was 9 years old. I was immediately put into E.S.L. class (not Language Arts or English class) until I was in Gr.9. When learning to read English, I remember writing down ways that I find was suitable for me to learn to read. To facilitate this, I would write "Pinyin" on top of the words that are difficult to read - for my own benefit, but my E.S.L. teacher suggested that I read using the dictionary (pronunciation) method with symbols I don't recognize, which was complicated. For this problem, I personally think that it would be better if my teacher appreciate my own learning method than doing something else that I don't find comfortable with learning.

In addition, as an immigrant myself, like McCourt, I can imagine the possible difficulties of teaching at Canadian or American classrooms. So there is still a lot for me to learn about the Canadian classroom cultures (even though I have attended Canadian institutions for many years). There are so much more to learn and explore when I do actually teach at a school, whether it is public, private or international!

Introduction

Hello everyone, this is my first blog for EDUC450B class at UBC.