Tag Archive | math

Well Internship Is Over, Now What?

I still remember my first day at university – really it feels like it was yesterday (just with a bunch of great events and memories that somehow happened in between there!).  But now, here I’m saying: It has been over two months since I completed my internship… WOW! To finally be able to say those words and knowing that I have 2 months left of university left… well… it’s absolutely insane! I can’t believe how my journey through university has gone by so fast (I truly am beginning to believe the expression “where did the time go?”).  

To comment on my internship, words cannot even begin to express how thankful I am for the people I was surrounded with during my experience.  As much work as it was, I enjoyed every minute of it.  And every morning, I didn’t wake up thinking “Ugh, now to go to my job… can’t wait till 3:30 comes!” Instead, I woke up every day excited for what was going to happen next and to surround myself with the positive support network that I had.  Yes, there were days when I could have wished for a few more minutes of sleep or even wished a redo for a day/lesson, but I always went to school feeling excited.  When end of December came, it just didn’t feel right leaving – I was very nervous to come back to school to be a student again!

So now that internship is done, I’m in my last semester of university.  To say the least, the teacher back to student transition has been a bit rough for me.  I feel like my rating as a student fluctuates constantly between a good student and the worst procrastinator in the world.  There are times when I tackle homework and actually surprise myself in what I have accomplished work-wise.  But then there are times when my mind starts to wonder from what my students are doing, how they are doing, and how much I miss teaching and being in the classroom.

Because I had taken a few summer classes during my summers, I am only taking 3 classes, and wow! What a huge help this has been (I definitely encourage everyone to do this!).  I am finally able to start relaxing and take a break from internship and I now even have time for a job (which is at the university).  Dealing with loans this year has been a huge struggle and now having the time to be able to work has been awesome! So right now, I’m working and in university and I’m still able to find the time to relax and actually blog (I have surprised myself with this, but I really do miss blogging – however now that I announce that to the world… I will probably fall off the band wagon again and not post for another month or two…).

Anyways, so now all that is left for my time at the university is to hopefully stay on my “good student” self rating and get through this last semester.  Also, it is currently job application time so wish me luck (which I will add is not easy! There are so many possibilities and considerations to make! Oh boy!)!  And to all you future educators and those graduating, good luck and I hope your university experience has been as amazing as mine! I hope you see you all on the flip side!!!

And hey! While I’m at it, I just wanted to thank all the people in my life for being so supportive and caring.  I know that having to deal with me at times can be difficult but it’s everyone in my life that has helped me get to where I am now. 🙂

The First Week – Huge Respect for Substitutes!

September 3rd-6th

So first week… what can I say? It had it’s ups and downs which is to be expected.  I began the semester by teaching Workplace and Apprenticeship 30 class (for those who don’t know, this is a grade 12 math class).

So, the very first day of class I only had my students for 20 minutes since we had an assembly part way through the class.  This was okay but it felt very chaotic.  I had a few things planned but with my mind running everywhere, I came off as very disorganized and did not have a teacher presence/authority.  The next day, however, I feel like my teacher authority came out when discussing the classroom expectations and rules and that I finally had established myself as a teacher (and not as some young person who thinks they can teach but can easily be run over by the students).

Things seemed like they were going well until my teacher had asked me to try “subbing” for one of her classes (don’t worry there was another teacher present!).  I asked what class it was and when she said “Foundations 10,” I figured “Hey, it’s grade 10 math! This should be a piece of cake!”   Was I ever wrong! The material that was being taught that day was converting units in the Imperial system (US metric system).  This was most definitely not on the top of my “most favourite topics in math” list.  In fact, I feel like I have put a block on this high school memory and I actually don’t remember learning it.  Asking my friends, they admit that they learned this material so I have come to the conclusion that I just chose to forget it because it was that horrid! So, if you could guess, this lesson did not go so well! I had trouble explaining the material and we actually ended up moving to the assignment and not finishing the examples (with the promise that my co-op would go over it the next day).  The one thing that I remember clearly in my mind is the fact that I kept trying to hint for the actual substitute teacher to take over (because he knew the material very well!) but he wouldn’t.  However, as sad as I had become about this lesson, this was a huge learning experience for me and I’m glad that he didn’t let me back out.  The next day I apologized to the class and taught the last example to the students. By doing this, I hoped that I could redeem myself as a teacher in those students eyes (which is huge I feel because I will be teaching them in about a month!).

With that said, my actual class went very well and I have already learned a lot! The sub day had me question myself as a teacher but you know what? We all have our bad days! It’s going to be okay and you know what? It’s only my first week! It’s not expected to go great! Internship is where you should be taking risks and making mistakes.  Just know that if you make mistakes, take them as a learning opportunity and don’t let it get you down!

“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.

“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 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).

IMG_1188

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.

IMG_1183

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.

Week One of Teaching

So, I was hoping to blog way more than what I have been, but wow! When I come home after school I am completely wiped out!  I have never been one to be in bed by 11, but since I have been teaching and observing, all I do when I get home is revise/create my lesson plans and then go to bed! Like holy wow! I was not expecting this and I talked to other teachers about it and they said that they went through the same thing and that our bodies just have to adjust (for a bit of assurance!).

Overall, it FEELS like this entire week has been a complete flop and I had a bit of an “Ashley” moment today after teaching one of my lessons. Even though this is something that I could have hid to make everything seem like it was going perfect, I feel the urge to make a confession to everyone explaining a not-so-great moment for me: So, I had a bit of a melt down (nothing serious though) after I taught my lesson today.  After all the stress of this week and the unexpected shortening class (further delaying my lessons and making it seem like more a flop than what it already was), I sat down in my chair and my eyes just welled up with tears.  Only a few tears managed to escape and I was able to recover quickly soon after once I got my mind focused on other things.  Fortunately, this happened during a break but I still feel that I should have handled that situation more professionally and should have been able to control my emotions.  On a good note, the rest of my day went fairly well! In a small way, I feel as though having that bit of a melt down made me feel a lot better (which is odd but I find this is the case quite often!… unfortunately).

So some of the stresses happened through this whole week mainly had to do with small things that went wrong in my lesson plans/teaching.  Sure some of these mistakes have been small and some were not in my control at all, but looking at all of these little mistakes it makes me think that I need a whole lot of improvement and even sometimes questions whether or not I can or should be a teacher.  A few of the mistakes or negatives about my teaching this week include:

– I need to learn to slow down when talking and take numerous short pauses to allow students to write notes and understand the material.

– I definitely need to work on my time management.

– Two of three of my math classes unexpectedly ended early (by about 5-10 minutes each).  I was unaware of this and I had planned for a 60 minute lesson (which is also wrong because I learned today classes are only 55 minutes… which I feel is strange!).  So, all of this combined has resulted in planning not going right and I feel my students are not understanding the material as well as I intended for them.

A few things that went fairly well this week include:

– Everyone seems to enjoy the activity that I created for the proof of the sine law for obtuse angles (cutting up the proof and having students put the proof into the correct order).  My partner has already used this idea (tried it out today) and my cooperating teacher has said that he would like to “steal” my idea.  This makes me think that my ideas are actually good, but I just need to work on putting them into practice (which gives me hope!).

– My questioning is starting to really improve.  Before I was asking very basic questions that were more of a nuisance to students and didn’t really get their thinking going or anything like that; and now, I am asking a variety of questions that are challenging the students thinking (which is what I was hoping for!).  I haven’t completely mastered this yet, but I feel that I have grown enough in this area that I can now move on to focus on other teacher aims and goals.

– One last positive is that I can remember most of my students names that I am teaching in period 1.  I have only had them for three days now (because of parent-teacher conferences) and I have been able to memorize all but a few students names (those who haven’t shown up at all yet!).  This has helped me tremendously because it shows my students that I am trying to make an effort to get to know them and teach them, and it also helps me with questioning.  When completing discussion-based lessons, if students are not taking part in this conversation, it is much easier to call out certain students when you know their names.

– My days go by SO fast! It’s amazing how an hour can go by when your teaching.  What feels like 15 minutes has actually been a whole hour!  I love how these days are going by so fast and I hope they continue to. 🙂

– I went to my school’s basketball game.  It was the junior girls playing at another school.  It felt great to be there and I found myself cheering for my team and getting angry every time the other team scored.  Unfortunately they lost but I felt a real part of the school by going!  Also, it’s fun and a great way to take your mind of things for a while.

For all of those pre-service teachers out there, I have a few pieces of advice:

1. Not all of your lessons are going to be awesome lesson plans.  In fact, maybe I should revise this to say “there is no such thing as a perfect lesson plan.”  Not everything is going to go as you have planned and there is always a better way of teaching a certain lesson so don’t feel bad if you don’t have a “perfect” lesson plan.

2. Make sure you talk to someone outside of your pre-internship about what is going on, such as family!  I haven’t talked to any of my family this week and I feel like I need to go on a rant to someone who doesn’t know my exact situation and knows how to comfort me.  I have tried talking to my partner and others who are closer to the situation and I feel that I am not getting my frustrations out (which may have led to my breakdown today).  They try to reassure me but they can’t quite calm me down and reassure me like my mom can.  So, those who can comfort you and talk you through things are good people to keep around because there will always be some sort of frustration that needs to be resolved.

3. Plan your lessons in as much advance as you can.  When you come home after teaching (especially in the first week), you will find that you are drained and don’t have the energy to look at lesson planning.  For me, I completed rough drafts of my lesson plans the weekend before and I still found it very hard to go back and try to think about completely finishing and fixing the final product.

4. Get lots of sleep and allow time for you to relax.  If you don’t do either of these, you will drain yourself and you won’t last the full three weeks (or internship or actually teaching!).  I plan on going swimming this weekend to help me relax so I am hoping this will help me clear my head and allow my body to relax and not feel over stressed/worked.

Overall, it was an okay week.  I am very excited to teach next week and hope that it goes much better than this week did.  I will be teaching Foundations Math 20 and Grade 9 Math!

But, that’s all for now, it is almost midnight on a Friday night and I am going to bed… who would have thought! But I’m wiped and struggling to keep my eyes open so I will hopefully blog early next week. 🙂