Reflection 3

Sylvia Duckworth. (2015, December 29). 6 Golden rules
for engaging students [Image]. Retrieved from: link.

How can we include everyone in class? This is such an important question that is difficult for some teachers to answer. In class we discussed the 6 golden rules for engaging student that give important guidelines to include and engage all students in class. Many of these guidelines highlight what we've discussed in the past few weeks; provide support to our students, foster a sense of competence, create positive relationships, etc. I will reference these rules when I am creating my lesson plans and when I am in the classroom, to ensure I keep my students engaged and maintain a positive learning environment.

How do we differentiate to allow for all students to participate and to understand? This is another important question for teachers. We talked about differentiating from different approaches which include differentiating: 

• The Content 
• by asking rich and open problems
• by including equity and social justice scenarios 
• by having students set personal goals and strive toward those
• by posing parallel tasks
• The Process (how they get to the answer)
• by letting students work in partners/groups for success according to the objectives of the lesson 
• by varying time according to the needs of the individuals 
• by modelling and using manipulatives and other tools
• The Product (what we expect them to do)
• by changing the amount of work/number of tasks that students have to complete
• by assigning appropriate roles in working groups 

Parallel tasks are sets of two or three tasks that are designed to meet the needs of students at different developmental levels, but get at the same big idea and are close enough in context that they can be discussed simultaneously. 

We were introduced to parallel tasks in class, and got to practice solving these open-ended questions ourselves. It was difficult at first, because I was not used to these types of math problems, and I did not know where to begin. It took me a while to feel comfortable, because I did not know which question to choose, or what process to use to solve it. When I realized that there were multiple answers, and different approaches I could take to find an answer, I felt comfortable diving into the problem and finding a solution. One problem I actually enjoyed was:

Woolley, E. © 2015

It was exciting because I had so many options. I could choose either question, as well as choose from a variety of answers. In this image, I answered both choices. One was more difficult than the other, but had the same big idea. 

We practiced coming up with parallel questions so that we understood how to create them for our own students. I found it challenging to come up with meaningful questions, and being able to differentiate, so that all students could be involved. I enjoy this because it is open-ended, and can be used as a good method of differentiation.

We went on to discuss how to take up these types of problems in class, because they are open-ended. We came up with Common Questions that were applicable to both question choices, so that all students were included in the discussion. For example, for the coin problem you could ask students questions such as:

1. What coin did you start with?
2. How did you decide what coins to use?
3. Could the value of the bear be an odd number? 
4. Did you find more than one answer? 

This way, students could think deeply about the problems, and the questions were relevant to both question options. In the image on the right, shows some of us practicing coming up with meaningful scaffolding and common questions that we can ask our students about parallel questions. This was a good activity, because it got me to think like a teacher and think deeper about what my students are learning, and how I can help them learn, but also understand the kind of questions that show me that they are learning.  

One final important thing from this week’s online modules is that there are multiple ways to solve a problem. Students can approach a problem in different ways, and as teachers we need to accept that students learn in different ways, so they will use different approaches and process to solve a problem. 

The video above talked about how speed does not determine intelligence. Teachers need to move away from the mentality that the students who finish a math problem first are the “smart” students. Teachers need to put an emphasis on the process, not the product. We need to remember that students need time to think deeply about the problem and find the best approach to solve it. Some students need time to analyze and understand the problem fully before trying to solve it. Math is not a race and we need to remind our students of this. We need to give our students time to solve math problems. 

Reflection 2

So far, this math course has been really great for learning about how to act as a teacher. Last year we focused more on instructional strategies and engaging activities, which was beneficial in our first year. I think focusing on our attitudes and actions this year is a good extension. Many people believe that teaching is just telling students how to do things, but it is so much more than that. It starts with our attitude, which I touched on last week.

This week we talked more in depth about having a growth mindset, which basically means being open-minded and overcoming challenges that occur. It is important to have a growth mindset when doing math because there are many challenges that make the subject frustrating. Both teachers and students need to be open-minded about the problems and be okay with making mistakes. With a growth mindset, making mistakes is a good thing, because we learn from these mistakes and become better. As teachers we need to help our students to have a growth mindset by having one ourselves. We need to model a positive attitude towards the subject, which will hopefully rub off onto our students. 

This video from this week's sessions describes the importance of having a positive attitude about our student's performances. 

 

I will take this important message to heart in my teaching practice. I will encourage my students to succeed. Not only do I have to have a positive attitude about math itself, but towards my students. If I tell them that they won't do well in math class, then they will become discouraged and fail. It becomes a self-fulfilling prophecy, which is not good in this context. Instead, I need to be encouraging and believe in my students, even when they seem to have given up on themselves. If a student becomes discouraged about a math problem because they found an incorrect answer, I need to change this negative perspective by asking myself and my students how we can take whats right in an incorrect answer. Using a growth mindset I can use the incorrect answer to explain the problem. As a teacher I will accept all answers to further the lesson to make students successful. This will show my students how mistakes are a good lesson for learning and show them how having a positive attitude is beneficial. Hopefully if I believe in them and continue to encourage them to succeed, they will do well. 

For example, in class we were posed with this math problem:

We had to find the which finger we would land on if we counted on our fingers to 1000. It was a challenging question for a few of us, but others figured it out right away. We started by counting to 10 on our hands.

 

Woolley, E. © 2015

I had trouble figuring out how to find out the solution without actually counting to 1000. I did not find the correct solution, I thought it would be the same finger as when you count to 10, but my peers found a different answer. Instead of giving up, I asked for help from my peers. As a team, we were able to figure out the solution and I was able to understand how we solved the problem. I hope to do this in class with my students, so that they are able to be challenged, won't give up, and be able to work together to find the correct solution.

Year 2 Reflection 1

This was the first week back at Brock for my final year in the B.Ed. program. This year we have another math class, where I hope to continue my personal growth as an educator of mathematics.

Natural Math. (2014, November 15). Math symbols in a
heart [image]. Retrieved from:
https://www.flickr.com/photos/26208371@N06/15798134722

I'm excited to learn more activities and strategies to get my students excited about learning math. This week we went over topics such as brain growth, math myths and stereotypes, and attitudes towards math. It wasn't surprising that the myths, stereotypes, and attitudes were all negative towards math. Many people, including myself, dislike math for many reasons. I found that many of the stereotypes where directed towards females being bad at math. I had hoped that this stereotype had disappeared since I was in school, but it is disappointing to learn that it hasn't. I know many girls that I went to school with, as well as girls in elementary school now who are extremely good at math, and who really enjoy the challenge of solving math problems. As teachers, we need to stop dividing our students' talents into genders. We need to realize that gender has nothing to do with understanding subjects or succeeding in class. The following video explains how ALL students can succeed in math.


This video explains how the brain is like any muscle in the body, and can develop and grow the more that we train it. If we encourage our students to challenge themselves in math class, they can develop their brains and in the end train their brains to be good at math. I think this is such an interesting video and will be useful for when I teach math, because I will be able to encourage every one of my students to challenge themselves. I hope to challenge my students so they work hard and become good at math with practice and perseverance. 

Another resource that I particularly enjoyed was the video Hollywood Hates Math. It was funny, but also eye-opening. It was a compilation of clips from various pop culture movies and shows that showed a negative attitude towards math. It was shocking to realize just how much our society dislikes math. We find it funny to talk about math in a negative way, but we don't realize the impact it can have on our students. When our students see these negative comments on their favourite show or movie, they tend to agree with it. We need to help our students see that math is fun and useful by having a positive attitude ourselves and by showing them positive attitudes in pop culture. 

This week was a good start to this year. I have learned a lot so far, and my attitude towards math is changing. I hope to continue to learn more this year and better myself as an educator.