Tag Archive | inquiry

“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.

“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

Learning Centres

Last week my partners, Allison and Ali, and I did a presentation on learning centres.  This was a short 10-15 minute presentation that we did in front of our ECS 350 class to help them develop a deeper understanding of learning centres and different ways to use it in a classroom.

Below is the handout that we provided for the class.  This handout includes what is a learning centre, pros and cons, implementation considerations, and examples of learning centres in different subjects.

Learning Centers Handout (Jan 31)

“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