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.

Week 12 Final Post

So I just finished my final week of classes. It's been a wild ride these last 12 weeks, and it's kind of a bittersweet feeling. I'm glad that the work is done, but I'm also sad that I won't see people until February after our praticum. I've definitely learned a lot in this class. I've met lots of great people, and found lots of fun activities that I'd love to use in my classroom. Unfortunately, I am in a Core French classroom, so I won't be teaching math. It kind of feels like a waste, since I spent 12 weeks learning about how to teach J/I math, and now I don't even get to use my knowledge. Maybe in my next practicum I will be teaching math, so hopefully I retain this information. At least I have this blog to refer back to to look at some of the strategies and activities to use in the classroom. 

Week 11 Reflection

This week we looked at quite a few online resources instead of the text book. This is because the focus was on using technology to teach math in the classroom. I think that this is a really useful topic, since we are being taught to use technology in most of our classes to make lessons fun for our students. A lot of our activities and resources in this class have been apps and videos to use in our classroom, but this week we went into a bit more depth about the resources we can use.

For one, we can use spreadsheet applications, which are interactive computer programs that allow information to be organized, analyzed, and displayed in the form of a table. I think that any interactive method is a good method, because it allows for differentiated instruction, and also tends to make learning more fun for students. Graphing scientific calculators can also be used, which is what I used when I was in school. I thought those were fun to use, but that was years ago, so I'm not sure in students nowadays would enjoy using them. We did a graphing activity, which was a graphing story about swinging. Graphing stories are short video stories that help students learn to graph on a plane. I like this activity, because it puts the problem into a visual, real-life context. For this particular problem, we had to find the height of the swinger's waist over 12 seconds. Watch the video below to see the problem and solutions:



Then we looked at another good program to use online, Desmos Graphing Calculator. We graphed equations like y = (x-2)^2 and played around with the graphing system. We changed the equation and talked about the transformations. This is a good resource to show examples to students, to explain graphing, and also a good manipulative for students to use themselves.

One activity that I really enjoyed was Prodigy Math Battle. Prodigy is an online game for students, where they are in a virtual world and they can battle opponents to win. However, to win the battles they must answer math questions correctly. What a fun and educational tool! Teachers can have their students log in and answer questions related to their unit that they are instructing. They have to go on the website, find the curriculum strand that they want and the specific topic. There are pre-loaded questions where you can select the test items that you want students to practise. This way teacher can create fun assignments that don't seem like homework. From there, the teachers can see their students' results and see where they need help.

Woolley, E. © 2015

We went over how to do this with the whole class, because it is such a good task!
As a class we decided to see the demonstration of how to create a math battle for our own classroom. We chose probability for grade 8, with the specific topic of complementary events. Then, we went through the questions a as a class to see how to use this website.

Woolley, E. © 2015

We also went over assessment of math assignments and tests/quizzes. This was extremely helpful, because in this class we have been focusing on how to teach math to students, but we have not yet talked about how to assess students' learning. Personally, I don't want to be a teacher who gives pop quizzes and tests every week. I want my students to actually enjoy learning, and want to come to class. I don't want to focus on grades, but on improving my students learning, and making math enjoyable for them. One of the resources I looked at before class was an audio file on Assessment strategies.

Another fun activity we tried in class was the finger counting challenge. The video below explains what this is. I like challenges like these because they require students to think about the solution and not just fill in numbers into a formula. Some student solutions can be found at this site.




Finally, we looked at another math challenge: Zombie Bridge Crossing
The video below describes the problem, and reveals the answer if you want to look at it. If not, I can briefly explain it, because I think it's an interesting problem to solve, and allows the students to use critical thinking.

Week 10 Reflection

We're nearing the end of the course. You can tell, because stress levels are high, as is the work load. However, I still manage to find time to write reflections of my math adventures. We focused on chapters 19, 20, and 21 from our textbook this week, which is a lot of reading. We mainly focused on data management and probability in our class. This is actually one of my favourite topics in math, which is really saying something, since (as I'm sure I've mentioned before) I do not really like math. 

Probability is almost always a hands on unit, using many fun manipulatives to model chance and probability. I think that this would be my favourite unit to teach, even if it is one of the hardest concepts to understand. Students need to understand the concept of odds, certain to, likely to, equal chance, not likely, and never. The least possible value of a probability is 0, which indicates that the event could never occur; the greatest is 1, which indicates that the event must always occur. If students do not understand value or fractions, they may not grasp this concept, so i must be sure that they understand this first.  

Theoretical probability can be confusing, because as the title suggests, it is based on theory. It is probability based on reasoning, written as a ratio of the number of favourable outcomes to the number of possible outcomes. To make it easier to see the possible outcomes, it is a good idea to model out all outcomes. You can use tree diagrams, which gives more details and maps out the probability of outcomes, or area models, which I find to be more confusing and harder to read. You can also graph out the possible outcomes, to find the chances or the outcomes like we did with our prof. He challenged us to pick a die to roll against his and see how many times we could roll a higher number. He had already calculated which particular die would have the highest outcome, so naturally we lost, because we just chose a die randomly. I think this was a good lesson because it proved that the theoretical probability matched the actual outcomes. 

We had a lot of fun activities this week, lots that I would use in my own classroom. Some were simple, and others were a bit more complex, but still lots of fun. For one, we had a spinner with numbers 1-4. We spun 10 times and calculated the outcomes based on our spins: 

Woolley, E. © 2015 

Another activity involved cards, as many probability activities do. Out of a standard deck of 52 cards, we had to write out the odds of various cards. For example, what are the odds of pulling a red card (26/52). We also did the same for a spinner and for rolling a die.

Woolley, E. © 2015

 We got to create our own survey and collect data. I think this is a great activity for students to use their own ideas to collect data. My group chose "how do you get to school" and used a pictograph to collect information. We asked our peers to select their answer and use a picture to response. An awesome, hands on activity for students! 

Woolley, E. © 2015

 Finally, we played a horse racing game, which was a lot of fun. We rolled two die and recorded the number rolled on the graph below. We rolled 52 times before we found the winner, which was #5. It was fun to see how chances worked. We had predicted that 7 would win because there are more variants of 7, but as chance and probability prove, the theoretical outcomes are not always what happens in practise. This was a fun way to play with students and show them theory vs. practise, and also a good way to teach students not to gamble! 

Woolley, E. © 2015

Week 9 Reflection

This week we discussed Measurement, which was covered in chapters 17 and 18 of the textbook. This was also the week that I got to present my Learning Activity Presentation.

First we talked about time, which I think is a fairly difficult topic to teach. The concept of time as a measurement is hard to understand, so it is a good thing that we reviewed strategies for teaching it. I think that the person who presented this topic did a great job. He made lots of jokes and really captured our attention, which in my opinion is a really good way to engage students. When I become more comfortable with math, I think I will try to incorporate this strategy into my own teaching. I think humour really shows students that you are comfortable being in front of the class and know the material well. It is also comforting for students to hear jokes because it eases the tension and reduces stress that students have with math.

I got to do my presentation, which was kind of nerve-wracking because I'm not the best at math. I think it went fairly well, I don't think I messed up at all. I went over perimeter, and using different manipulatives for measuring length. I think this was a really good experience, because it gave me the opportunity to practice teaching math in front of people. It really got me out of my comfort zone and ready to start teaching math, which I think was a great assignment. I talked about using nonstandard and standard units to measure length and perimeter. I had no idea that there was such thing as nonstandard units, but i think its a really neat concept to teach. It helps students understand the concept of measuring length without attaching it to a standard unit of measurement. Some of my favourite nonstandard and standard units of measurement are pictured below:

Woolley, E. © 2015
Straws, linking blocks, toothpicks, centimetre cubes/ten blocks, string, measuring tape, and a ruler.

 I think that I was well prepared and had an interesting activity planned. I didn't get it from the textbook, because there were no activities planned for teaching perimeter. I found it at this site which listed a few hands-on activities for students. Students had to write their name in block letters onto centimetre grid paper, and then measure the perimeter of each letter and full name using nonstandard and standard units. I liked this activity because students got to be creative and also to practice measuring with different manipulatives. Below is my example that I did with my name:

Woolley, E. © 2015

The other two presenters talked about area and volume respectively. They both had good activities that helped to highlight the concepts of area and volume. We went over some more good hands on activities that I hope to use in my classroom. The one I liked was a real-life activity for calculating volume. We got an empty Kraft Dinner box and centimetre blocks. We used these standard units to measure and calculate the volume of the box. I liked this activity because it was visual and hands-on, unlike the worksheets and questions I had to do when I learned volume. This is better because students can actually see how volume works.

Woolley, E. © 2015 

We did some more fun activities after the presentations. We read a short story about the Pythagorean Theorem, and did an estimating activity. We had to estimate how far we could jump, and then measure it. It was surprising how much fun we had jumping and competing, so I can only imagine that students would have just as much fun with this activity.

Finally, we watched a funny video featuring John Green, one of my favourite authors, explaining 36 unusual units of measure. It was funny, and educational. I would show this video to my class, have them take notes on their favourite obscure units of measurement, and then measure objects as a fun activity.