“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:



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.


“Blog About It” Response Journal #7

Question One:

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


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?


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.

“Blog About It” Entry 6 Part B

Part i) Reflection on “3 Big Questions” Blog

I completed my pre-internship practicum last Thursday and all I can say about it is WOW!!  The amount that I have learned in my three years in the education program does not even compare to what I have learned and how I have grown in this three week block.

Looking back at my initial responses to the “3 Big Questions” in Part A of the Entry 6 blog, I can say that my answers now aren’t that much different from three weeks ago.  The only big difference I would say is that I would put more emphasis on some points and less on others.  One example is in the first question: What do you think is the purpose of field experience (i.e. pre-internship practicum, internship, etc.)? In my response, I do not differentiate which of the 5 points are more prominent than others.  Now, I believe that there is one point in particular that is the most important purpose of the field experience: “it’s a chance for us to practice teaching and work towards becoming the teacher that we imagine ourselves to be.”  The whole time during my experience, this was the most important factor that I considered and always kept in mind while teaching and lesson planning.  In fact, the other purposes that I mentioned passed through my mind only a small fraction of the time when compared to how often I thought of the above purpose.

Maybe one change that I would make to the above statement is I would like to reword it: It’s a chance for us to experiment and try new things that will help us work towards becoming the teachers that we imagine ourselves to be.  I feel that the previous statement doesn’t put enough emphasis on the “trying new things” part which I believe now is a huge part!  During my pre-internship, I decided that now would be the best time to try new things since I would only be there for three weeks so I couldn’t mess things up horribly and that if I did mess up, there would be an experienced teacher to help me out.  There are a number of things that I tried out in the grade 11 classroom that I was teaching which I was very unsure of the results (but turned out pretty great!):

Note: I am used to teaching and learning math through direct instruction so even though this may seem like small things to you, they felt like huge chances to me! 1. Instead of teaching proofs by writing notes on the board and trying to explain it, I did an activity with them where they had mixed up parts of a proof and had to put it together in the correct order (kind of like doing a puzzle).


2. I used a manipulative for teaching the ambiguous case rather than just drawing diagrams on the board and explaining.  Students paired up and each group got one manipulative.


This idea was shared from Christine Schmidt’s website.

3. As an introduction to a new unit, I used an inquiry style introduction to find out where my students were at.  In this activity, I gave students a list of equations and a blank chart with 3 categories.  At first, I would tell students which category an equation fit into and they would have to guess what the category was.  After a while students began to realize what pattern was developing in two of three categories (the third because this was a “neither” category so there would have been no pattern) and then they would tell me where the rest of the equations fit.  From this I was able to see what students could remember from previous classes (which I found out they knew equations from the first category but not from the second).

If I had to change the emphasis placed on each of the 5 purposes that I had listed, going in order from most important (1) to the least important (5), I would say:

1. ” that it’s a chance for us to practice teaching and work towards becoming the teacher that we imagine ourselves to be.”

2. “gradually get used to the idea of teaching and makes us aware of some of the things to expect when we begin teaching.”

3. “allows us a chance to take what we have learned in our classes and actually apply that information into the classroom.”

4. “observe others and expand our ideas of and knowledge about teaching.”

5. “increase PLN (personal learning network) and get our names out in the schools.”  (This one may vary depending on which field experience you are completing – if you are in your internship this will have a higher importance when compared with your first field experience where you are just observing teachers).

Part ii) Reflection on the quote from Dewey (2003)

“Working with preservice teachers can be puzzling and surprising, particularly because they are students at the same time that they are learning to be teachers… I offer the following suggestions for teacher educators in assisting preservice teachers to discover their teacher selves. It is important to help students identify inconsistencies between their beliefs and practices and to discover counter examples to strongly held beliefs. In addition, preservice teachers must learn to assume personal responsibility for their actions and performance and not blame the students or others for their problems. To be a learner requires the consent of the learner (Loughran & Northfield, 1996). Therefore, it is essential that the learner is open to learning and seeing multiple perspectives. It is important that preservice teachers acquire a discovery, problem-solving mode that allows them to inquire and examine their teaching and the students’ learning through reflection and inquiry. I have learned that for the inquiry–reflection cycle to successfully become a habit of mind, it is important to help students develop the following attitudes and dispositions essential for reflection: open-mindedness, responsibility, and wholeheartedness (Dewey, 1933).”

The key message that really stands out to me is the importance of challenging and reflecting on one’s experiences and thoughts to help  that person discover his/her teacher self.  I can say this from my own personal experience, a recent example being from my pre-internship where I found that one of the best ways that helped me improve as a teacher was to reflect and think back on my lessons and think about how I could improve, what went well, what needed to be changed, and whether or not my teaching strategies were effective.

Also, during my post-conference with my cooperating teacher, he challenged my thinking and questioned some of the methods that I used to teach a particular lesson which really got me thinking about aspects of my teaching that could be improved or changed and whether or not they were best for the students and not just best for me.

Another key point hit in this quote is when Dewey states “To be a learner requires the consent of the learner.”  This can be said by the old saying that you can lead a horse to water but you can’t force it to drink it.  Same goes for teaching and learning; if a student is unwilling to learn, they won’t and you can try all you want to make them learn but the only way that they will is if they want to.  So, this is my question now: If students are unwilling to learn, how can we encourage them and help them to realize that they want learn and that it would be a great benefit for them to do so?  And of course I know that we learn all the time even if we are unaware of it but what about learning in schools?  How can we help students want to become  and realize that they are life long learners?


Quote taken from: Freese, A. (2006). Reframing one’s teaching: Discovering our teacher selves through reflection and inquiry. Teaching and Teacher Education, 22(1), 100-119.

“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 (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.


your high school math best friend, Ashley

Assessing Mathematics Reflection – Blog About it PDR #4

Thinking back to high school, I can only think of being assessed in two different ways that were memorable: homework and written tests/exams.  Of this three, I would have to say the most memorable/vivid form of assessment for mathematics would have to be written tests/exams.  This brings thoughts mostly of good experiences that I have had with this form of assessment in my high school mathematics classes.  This is because in high school, I was one of those students who excelled at writing tests and exams.  Also, I never saw a problem with having such a limited variety of assessments because I never knew there were different ways to assess mathematics besides written tests/exams (and homework) until I enrolled in education math classes in university.

Online Portfolios

After the presentations in class on Tuesday, I realize now that there are two other ways that a few of my high school math teachers attempted to assess me: investigation and portfolios.  However, one of my teachers only attempted investigation once and the portfolios were very informal and not efficiently used.  It wasn’t until I had completed my presentation on portfolios that I realized one of my high school teachers had used this form of assessment.  This is because I had previously thought that portfolios were either only art portfolios or the professional kind of portfolios that contained your resume, cover letter, any awards/accomplishments, etc.  So basically, the type of portfolio that I could take into an interview, say for teaching, and show this to my future boss to help increase my chances of being hired.  Now, I am aware that there are different types of portfolios, including student portfolios, and what you can include can vary depending on what your purpose is and what you want your end goal to be.  A few other bits of information that I had learned about portfolios in a math class includes:

1. How you can use portfolios in math – create a portfolio for a famous mathematician, see a student’s thinking process and understanding, provide evidence to parents of their child’s learning and allow them to get involved with their students learning, and to upload assignments on (for online portfolios; this could include presentations, videos, and/or VoiceThreads).

2. What you can include in a portfolio – vocabulary words, videos/presentations, homework, tests/exams, reflections/journal entries, and/or any resources that the student found helpful with math.

3. Advantages – using portfolios in a math class can definitely be more advantageous than not in a math class.  These can be used for showing strengths and areas of improvement, best work, getting parents involved in students learning (for online portfolios), for checking students understanding of materials (through things like reflections), and they can be used as an end of unit/year review, assuming that homework and/or tests have been collected in this portfolio.

During presentations, I had learned about many more different methods of assessment, two in particular where I learned the most were: oral presentations and reports, and anecdotal records and checklists.

Oral Presentations and Reports

I already knew what oral presentations and reports were, but what I didn’t know about them is
1. When to use this method – when opinions need to be shared, at the conclusion of a research as a way of sharing findings, and after content has been explored or experienced.

2. When not to use this method -at the start of a unit or when time is of the essence.

3. Advantages of using this method – builds students communication and public speaking skills, allows creativity and personalization, integrating language skills, and it can be interactive.

4. Disadvantages of using this method – can be stressful for students who are shy, time consuming, can be biased and may not be completely accurate (teacher must mark everything at that time or he/she may forget something essential).

Thinking about this method, I’m not 100% convinced I would use this often in my classroom.  I suppose it is hard to tell until I become comfortable with the idea of it in math and can think of projects that my students can do that can include this method.

Anecdotal Records and Checklists

First of all, I had no idea what anecdotal records were (although I had a slight idea).  In Kelsey’s presentation, I learned that anecdotal records are written observations of what you see taking place in your classroom as students are working.  So, a few other things that I learned about anecdotal records and checklists are:

1. Advantages of this method – facilitate review of assessment and curriculum, provides cumulative information on student learning, and provides ongoing documentation of learning that may be shared with students, parents and teachers.

2. Disadvantages of this method – can be time consuming after class and requires planning and preparation.

3. When to use this method – use to assess the understanding of mathematical concepts and while students are working (both individually or in groups).

I would definitely use this method in my classroom.  In a way, I feel that it is something that we already do when planning our lessons and walking around checking on student work and understanding, just minus the writing notes down on a piece of paper or checklist.

 Purpose of performance-based assessment and  how they connect to ideas of assessment for/as/of/ learning.

From what I’ve learned, performance-based assessment checks a students skills and understanding rather than just checking if the student can compute a correct answer.  It can be used to check if students are at the appropriate achievement level and let you know that your class is ready to move on to other material.  Although many performance-based assessment methods can be time consuming, it is definitely worth the time to use because it checks these important things that simple testing cannot.

In my opinion, most of the performance-based assessment connects with the assessment as learning, although a few fit with assessment for and assessment of learning.  For example, entrance slips can be used as a diagnostic so it could be considered assessment for learning, interviews and anecdotal records and checklists check for student understanding throughout the unit/year, and rubrics and rating scales assess at the end so this is a form of assessment of learning.  However, any of these assessment methods can be manipulated to fit any of the assessment for/as/of learning; so really when you think about it, performance-based assessment connects with all the ideas of assessment and learning and it is definitely worth while to do as students can benefit greatly from this.


In my classroom, I would definitely use performance-based assessment to assess my students.  It provides much more detailed feedback that my students and myself can benefit from rather than just assessing students using tradition methods of testing and homework checks.  This assignment was definitely an eye opener of how different types of assessments can be used in math and for all of you math teachers out there, there are more ways to assess students than just testing! Don’t be afraid to try new things.  These assessment methods are definitely a great starting place at changing the perception of what a typical math classroom is.

“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.


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