Tag Archive | math education

“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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Social Justice Unit Plan

Here is a unit plan for incorporating social justice into mathematics:

understanding-by-design-unit-template (1)

In this unit, students will research a social justice issue.  They will create a report (which they will actually send to someone) and a presentation on this issue and possible solutions to this issue.  The requirement is that they must use mathematics somewhere in their report to help support their argument or issue.

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 #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

Differentiated First Nations Lesson Plan – ECS 350

ECS 350 First Nations Lesson Plan

Above is the differentiated First Nations lesson plan that my partner and I did for our ECS 350 class.

In this lesson plan, our plan was that we would get students to create a hand drum (including making hide if possible, but with the time we just gathered all the supplies) and then use this to help in math.  This first part could be done in an art or music class if possible.  The hand drum creates a circle so we would use this to discuss the grade nine unit on circle properties including central angles and inscribed angles.  While discussing the properties, students would draw/paint on their hand drums so that they have a visual representation of what they were learning.

The process of creating this lesson plan was both difficult and relatively simple.  Differentiating the lesson plan was fairly easy because for the most part, many of the students had many adaptations that were common with one another.   However, there were a few that we found very difficult to try to incorporate into our lesson plan and left out (only some though!).  Another difficulty, that was also easy in a way, was deciding how to incorporate First Nations culture or Treaty education into math.  In a way it was easy because I  feel that the education professors do a very good job at trying to make us aware and understand how to incorporate treaty education into math.  We have had a few presentations and work shops where we have learned different ways to include First Nations content and treaty education into mathematics.  The idea that we had used for our lesson plan came from a couple presenters from Leading Thunderbird Lodge, which is a residential youth treatment center for male youth.  This idea that these presenters had shared with us had originally been shared with us to fit the grade 8 curriculum which is where Ali and I had run into a few problems.  The ideas presented had to do with labeling a circle and this idea would have worked great.  However, since Ali and I are secondary education students, we tried to adapt this idea to fit into the 9-12 curriculum.  We found our outcome in the Shapes and Space unit in the grade 9 curriculum but it didn’t exactly fit with the idea presented to us.  So, after some time, Ali and I came up with the idea to change the labeling and use of the hand drum.  Instead of labeling the hand drum, we would get the students to create a number of subtended angles and their corresponding central angles.  By doing this, students could create their own generalizations about the relationship between these angles and therefore have a deeper understanding of the content.  This also creates patterns and allows students to be creative if desired.

Ali and I were very happy with the way our lesson had turned out.  However, we and others determined a few minor changes after a completing a lesson study with other classmates.  During this study, we came up with the following changes to the lesson plan (which we have not changed in the lesson plan that we have uploaded):

1. In Essential Question 1, this should be “what is the meaning of a hand drum and what is it used for?” rather than “what is a hand drum.”

2. Instead of labeling their hand drum, tracing their hand drum, and then drawing inscribed and central angles on this paper, we would get students to just draw these angles directly on the hand drum (and of course in different colours so they can tell apart each angle).

3. Also, we should include questions about what would happen if the top point of the inscribed angle changed while the bottom two points stayed the same? (they should find that the angle stays the same no matter where they move it).

4. Include graphic organizers.