Tag Archive | reflection

“Blog About It” Response Journal #8

I am now nearing the end of my EMTH 350 course.  Looking back at all the blogs, my most favourite blog was “Blog About It: Entry 6 Part B.”  I really like this blog because I actually connected what we have been talking/blogging about to what I actually did in my pre-internship.  In this blog, I am making connections and I have a better understanding of the teacher education program.  Also, reading it over, I have a flash back of my pre-internship experience and think about all that I have learned and how I have grown/changed.  I love to reflect and think back about what has changed and what hasn’t.  So of all the “Blog About It” posts, entry 6 part B was my favourite.

If I could go back and redo any of my blogs, I would definitely redo the first blog.  Looking back at it there are a few changes that I would like to make and add a few things, especially after my pre-internship.  Also, I would just like to rewrite it in general.  Reading it over, I can see that I made a few grammar mistakes and there are a few wonky sentences.  Lastly, I would redo this blog entry because I feel like I could have expanded more on a few ideas.  I can’t remember if there was a word limit, I know for sure that there was a minimum but if there is no maximum, I would definitely like to expand on a few points.

Although this is the first blog is the one that I would like to redo, it was also one of the blogs where I feel that I have learned the most about myself as a teacher and learner.  The main reasons for this are mainly because it made me question what the purpose of teaching math was, how to actually teach math, and how my past experiences have shaped how I thought of teaching math.

Create a blog entry you would like to have been asked to respond to but were not; after creating the blog entry question, respond to it.

– How did your pre-internship go? Did you try any inquiry assignments?  What did you do and how did it turn out?

Pre-internship was great! I learned a lot and it was an enjoyable experience overall.

Throughout my pre-internship, I did try two inquiry lessons.  The first inquiry lesson that I taught was an introduction to the unit of using the law of sine and the law of cosine for obtuse triangles.  In this lesson, I wanted students to figure out the relationship between the sine/cosine/tangent of an acute angle and the sine/cosine/tangent of it’s supplementary angle (obtuse angle).  So, I gave students a chart that had a number of acute angles in the first column and instructions of what to do with that acute angle going across the top row.  Ex:

supplementary angle worksheet

Originally, we had this worksheet in a different order.  So, we had them do the sine/cosine/tangent of the angle first then do it of the supplementary angle.  Students didn’t see the relationship of the angle and it’s supplementary angle initially until I pointed it out.  However, I was able to reteach this lesson and I changed the table to look like the document above.  Immediately after filling in the values, students were able to make that connection since the values were side by side.  In the end, both classes ended up realizing the pattern was that the sine of an angle is equal to the sine of it’s supplementary angle and that the cosine/tangent of an angle was equal to the negative of it’s supplementary angle.  As a note, the second lesson definitely went better than the first so I am glad that I had made that change.

The second inquiry lesson that I had taught was the ambiguous case of the sine law.  With this lesson, I gave models of an acute ambiguous triangle:

IMG_1183

 

Students were also given a chart where they had to determine the height of the triangle, whether or not the value of “a” was larger than, equal to, or less than the height, how many and what type of triangles were created, and then they had to draw the diagrams.  In this lesson, students discovered that with acute ambiguous triangles, that if a<h, then no triangles were created, if a>h but a<b, then two triangles could be created, and if a>b, then only one triangle could be created.  Overall, the lesson went fairly well.  However, the students got hung up on trying to determine the type of triangle that was created.  So, if I were to change the lesson, I would definitely take out the part where they have to determine the type of triangle.  This would definitely have saved time and allowed them more time to work on examples and the assignment.

Overall I would say the lessons were a success but I wish that the students had more time to do examples and practice using the material that was just learned but unfortunately we were under a deadline and had to assign whatever homework wasn’t done in class (which was difficult since a majority of students did not complete their homework at home – and I knew this and was trying to avoid it).


Looking back on the EMTH 350 course this semester, describe two topics (areas of interest) you would like to have focused on more in this course that you feel would help shape your growth and learning in becoming a mathematics teacher.

1. Flip Classroom

2. Inquiry in math.  Just kidding! We did a lot of that.  I would say creating assessment for students and giving feedback.


Looking ahead to internship in the Fall, describe two overarching goals you have (or want to) set for yourself. (If possible, connect these two goals to learnings you have had in this course or in your teacher education program in general.)

1. Trying inquiry at least once a unit (maybe once every week or two – even if it is just small)

2. Work on differentiation and try tiered assignments.

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“Blog About It” Response Journal #7

Question One:

Do you believe that working with others on lesson planning is beneficial?  Why or why not?

Reason:

A huge part of this course had to deal with group work and something that is gaining increasing interest is doing team teaching and classroom swaps.

Question Two:

We have seen four ways of conducting a lesson study: video recording, self reflections, group reflections, and whole class reflections.  Of the four, is there one that you feel is the most beneficial to you? Why or why not?

Reason:

Lesson studying is an important process of growing as a teacher and improving one’s self.  Finding that “best way” to lesson study is important and can be very beneficial.

My Teaching Philosophy After Pre-Internship

After completing my pre-internship experience, I am now faced with a question: Has my teaching philosophy changed? My answer to this question is yes! There are things that I definitely feel more stronger about, that I am now questioning, that I know have realizations about, and that I would like to add.

One thing that I..

1. Feel stronger about:

I definitely have a stronger belief in the fact that teachers need to help students understand subjects (like mathematics) rather than memorize it.  For some subjects I know that this could be hard but up until I started taking education math classes, I never thought that there was a way that we can actually teach and learn math so that it can be understood and be connected to real life rather then through memorization and being basically spoon fed the information.  Now, I realize that there are always ways to help students understand material and not just memorize it (although sometimes it will require a bit of work!).

2. Am I now questioning:

I question my understanding of putting in 100% of my effort to try to help my students learn and succeed in their schooling.  During my pre-internship, I noticed that there was on average one student in every class where the teacher just didn’t even try to get them to write notes, do the assignment, or get them off of his/her phone.  They basically said that as long as the student wasn’t disrupting others, they could just sit there and do nothing.  This makes me wonder at what point do you just give up (or I apologize maybe this isn’t the correct term to use…) on a student so that way you aren’t slowing down the rest of the class.  It also makes me wonder if this same way of thinking will happen to me?  Will I just allow a student to sit there and do nothing and refuse to learn?  I just don’t see the point in being in school if you are just going to sit there and do nothing.  But now comes a question that I now have: Is it appropriate to ask a student to drop a class if they refuse to learn or do anything in that class?  Or can I ask them why there are there in that class if they are just going to take up space and not do anything?

3. Now realize and would like to add:

I now realize the importance of allowing students to individually practice examples of the material that we have just covered and having the teacher walk around checking for understanding and clarifying any questions.  

I unfortunately learned this the hard way in my pre-internship.  In one of my grade nine classes, we had spent 3 and a half days on one section of the text book (which I personally feel was quite a bit of time to cover that one section which built off of the previous section so they should have had a really good understanding of the material).  In the first day and a half, we spent the class time taking notes and doing A LOT of examples as a class.  Everything seemed to be going fine; many students were answering questions and shouting out answers so I genuinely thought that they would be ready for a quiz after some practice.  So, the next two days I had spent with them doing an assignment and a worksheet.  On the fourth day, we had a quiz and I was very surprised to see that a lot of students were struggling with it!  I knew that there would be a few students who would struggle with it but it seemed like more students were struggling with this than I had expected. 

After this, I had realized my one flaw that most likely had the biggest impact: I didn’t get to do much one-on-one work with my students and be able to check if ALL students were understanding the material (I couldn’t even get much one-on-one time with the students during the assignment and worksheet time because I was trying to get students who had missed previous classes caught up). 

Also, by being able to walk around and check students work, this would have been a great classroom management strategy to get the students writing down notes and all the examples (which I found out many were only watching the board and answering instead of taking notes as well).

Also, just because students are either quiet or many shout out the answer doesn’t mean that they completely understand the material which is another reason why allowing students to do individual work while the teacher is circulating the room is important.

So clearly, I now would like to add to my teaching philosophy the importance of allowing time for students to do examples and work individually while you walk around and check their work.  Big lesson I learned there.

4. Would like to add:

I actually no believe in tiered assignments.  I tried this out during my pre-internship and it actually turned out to work fairly well!  The students have done tiered assignments in that class before so they had an understanding of the expectations and what to do.   I did struggle with actually creating the assignments because I didn’t really know what assignments would be considered equal amount of work or time so that students didn’t chose which assignment was faster or shorter. 

What I would do now that I didn’t  realize until after but is I would do all the questions first (which I did) and then I would assign a mark to each question.  Then, I would make one assignment and then use the total value of marks to create the next test.  When doing this in my preinternship, I just looked at the questions and just kind of randomly picked the number of questions and made it all roughly the same number of questions rather than the same amount of time or work.

“Blog About It” Entry 6: Part A – 3 BIG Questions

Three BIG questions about field experience and the role of teacher education:

1. What do you think is the purpose of field experience (i.e. pre-internship practicum, internship, etc.)?

I feel that field experiences serve many purposes that are all important.  The first is that the field experience allows us a chance to take what we have learned in our classes and actually apply that information into the classroom.  Throughout the past three years, there has been a tremendous amount of information that we, as teachers, need to know.  We can memorize and try to understand this material as much as we can but the best way for us to actually learn and understand this material is by experiencing it in the classroom and putting it into practice.  I can say that this is true for a fact because I’ve been through this.  One specific example was ECS 200 and 210.  There was a lot of information that, sure I thought was important, but I didn’t fully grasp the idea of what this might look like and how it would affect my teaching.  It wasn’t until ECS 300 when I got to teach is where I saw a lot of this information coming back to me and finally being able to see how it impacts the classroom and teacher.

The second purpose is that it’s a chance for us to practice teaching and work towards becoming the teacher that we imagine ourselves to be.  Also, it gives us a chance to try new things (ex. teaching styles/methods, classroom management, etc.), see what works and what doesn’t, and make mistakes while we still can and have someone to help us out if things get rough.

Another purpose includes being able to observe others and expand our ideas of and knowledge about teaching.  Sometimes, you don’t get to experience a wide variety of classrooms and teaching styles, especially for those in small schools.  Thus, being able to experience different classrooms and different teachers expands our knowledge of more current teaching practices and the different methods and practices that occur that differ from our own schooling experiences.

Being able to increase PLN (personal learning network) and get our names out in the schools is another purpose of field experiences.  Being in a school, there are many teachers and staff that you can become acquainted with and add to your PLN.  PLN’s are very important as the people in this group share information with one another and help each other out if needed.  Also, getting your name out and around to different teachers and administrators can increase your chances of getting a job.  Listening to many stories from interns and new teachers, their field experiences (mainly internship) got their name out to different people and many have been given high recommendations and some even got hired at their internship school immediate after graduation!

Lastly, then field experience allows us to gradually get used to the idea of teaching and makes us aware of some of the things to expect when we begin teaching.  Gradually get us used to the idea of teaching is important because that way it doesn’t feel like we are being thrown into teaching and become overwhelmed.  Being aware of what to expect and have few surprises will help increase the likeliness that we actually become great teachers and that teaching is something that we make a career of.  Statistics say that the first 5 years of teaching is the most difficult and this is when many teachers quit their jobs and move on to other professions.  A huge factor of this loss is because of the stress and complications that teachers had not foreseen and then become greatly overwhelmed and stressed.  Field experiences allows us to practice, observe, and become aware of and prepare for some of the complications, stress, and any other troubles that they may face in the future.

2. What roles does (or should) a teacher education program play in the process of becoming a teacher?

Just like the field experience, the teacher education program provides us with the opportunity to prepare for and work towards becoming the teacher that we want to be.  It also provides us with the information that will help us succeed as teachers, to be the best we can be for our students, information about students and their learning so that we can prepare to educate our students and help them to maximize their chances of success in school, and in life.

The teacher education program also allows us the opportunity to put this information to the test by applying it to actual teaching experiences.  Through these experiences, we are also provided with the opportunity build our own teaching philosophies and theories, to put these into context, and make changes and amendments to work towards perfecting these philosophies and theories.

Also, the teacher education program challenges our current views of teaching and education.  Teaching and education is rapidly evolving and changing; thus, it is important that we constantly challenge our ways of thinking and think of new ways to better ourselves and make our teaching more effective and efficient so that students can maximize their learning experience at school and make it more enjoyable.

3. What do you already know now about being a mathematics teacher that is unlikely to change through your upcoming field experiences (i.e. fundamental beliefs, values, commitments, etc.)?

There are a few things that I can be certain about being a mathematics teacher that is unlikely to change through my upcoming field experiences.  This includes:

1. As a mathematics teacher, I need to help my students understand math, rather than memorize it.

2. Rather than just the answer, it is more important to teach and assess the thought process and steps of a solution.

3. As a mathematics teacher, I need to be 100% committed to teaching my students, be there if they need help, and provide them with everything they need to help the succeed.

4. In mathematics, not every lesson has to be inquiry-based.  There are many factors that can affect this such as timing and the type of class.

“Blog About It” Entry #5

Dear high school math best friend,

How have you been? I know it has been 4 years since we last talked, but I was watching two videos for my education math class at the University of Regina and I began reflecting about my old high school math class and immediately thought of you!  These two videos, which can be found at http://www.learner.org/resources/series31.html# (videos #9 Case Study: Group Test and #10 Teacher Insights 9-12) if you’re curious, videotape a variety of math classrooms and discuss the strategies used in each.  I would definitely recommend you watch these videos because, even though they may seem a bit retro, they show different views of what a math classroom looks like.

Watching these, they made me think of our math classes.  Do you remember how boring our class used to be?  How everyday, we completed the same routine over and over again where we would take notes, do examples, and then do homework?  For any kind of assessment and evaluation in that course, it was all individual work and we were expected to be quiet and not talk with one another?  Well, in the video #9, students are doing group tests and in video #10, students are working in groups and doing inquiry activities and presentations rather than just the boring usual homework.  Not once do we see students doing anything that we had ever done in our classroom.

I don’t know if you can, but I can’t believe it!  I never knew there was a different way to teach and learn math until I watched these videos.  It makes me wonder how much more enjoyable our math classes could have been for not just us but for everyone!  Imagine being able to do group tests, talk out our answers and questions with one another, and be able show our understanding and knowledge in a variety of different ways.  I know that written exams were not your strongest point, even though you were very intelligent in math. Do you feel that doing something like this would have made math more enjoyable and successful for you, and as well for others?

In video #10, the teachers use two different techniques that I envy and wish would have been implemented in our math class: 1) coloured pages which create organizers for us and provide us with information to help us understand the material and study; and 2) being tested on more than just getting the right answer.  The coloured pages seemed like great ways to stay organized, study and learn from, and deepen our understanding of the concepts that we were learning in that class.  Organization is something that I definitely need and possibly could have helped you as well.  As for being tested on more than just getting the right answer, I know that this would definitely help me out since I always made silly little calculation errors which caused me to lose quite a bit of marks.  Also, this shifts the emphasis of the answer being important to the steps of getting to the solution and students thought process.

I hope to hear back from you and I definitely encourage you to check out the videos! I think that your mind will be blown when you see how different math classes can be.

Sincerely,

your high school math best friend, Ashley

“Blog About It” PDR Journal (Entry #3)

Reading the article, “Understanding Change Through a High School Mathematics Teacher’s Journey to Inquiry-Based Teaching,” by Olive Chapman and Brenda Heater really reinforced many of my beliefs about teaching and learning math.  There were only a few exceptions that made me feel a bit skeptical of the article and the message that was being conveyed.  One example was when the authors discussed Brea and her “change.”  They even stated that Brea was a “unique story of change” (pg 448) and the fact that they only had one teacher’s experience had me quite skeptic.  I personally don’t believe that everyone will change as fast as Brea did, especially the teachers who have been teaching for many years.  To get teacher’s to admit their own challenges/problems might pose as a difficult problem and could leave some teachers more upset than anything.  So, my question is, how do we make these teachers realize the way that they have been teaching may not have been as effective as it could be?

Other than that, I agreed with most of the article.  There were a few points, in particular, where I felt most connected to Brea.  The first was the description of her initial thoughts before she developed a better understanding and awareness of inquiry.  In the article, Brea thought that “[her] job was to simplify math” (pg 450) and that is how I still believe I should be teaching math with the addition that it should be for understanding as well as simplifying it.

Also, another point where I felt connected to Brea was when she stated: “At first I kept longing for someone to just show me what inquiry was” (pg 454).  Since I have been introduced to the concept of inquiry, I continuously wanted (and still want) teachers to show me what inquiry looks like and how I can use it specifically in my classroom.  I believe that in order for me to have a better understanding of inquiry, I will have to work at this and design inquiry activities on my own in order to develop this awareness of inquiry.  This, however, is going to be my greatest challenge.  My previous beliefs and ideas about teaching math were the same as my high school teacher and every time I am introduced to a new concept or get slightly out of my comfort zone, I immediately want to go back to these thoughts.

Also, I believe they hit a huge point when they discussed reflecting.  I’m a huge believer in reflection (as I know many people are not such a fan of this), and I feel that it really helps me to learn, grow, and become more aware of what’s working and not working in my classroom.

References:

Chapman, O., Heater, B. (October 7, 2010).  Understanding Change Through A High School Mathematics Teacher’s Journey to Inquiry-Based Teaching.  Journal Math Teacher Education, 13(6), pg. 445-458. DOI 10.1007/s108757-010-9164-6