Final reflection

This was the final week of our math course for Year 2. It's amazing how fast time flies when you are busy. We've gone through so much information and I have learned a lot over the past few weeks. This week our final topic was feedback and assessment; two very important concepts.

I have noticed that many people don't understand how to give meaningful feedback to students; they give marks, but don't tell students how they can improve for next time. Feedback is essential for student learning, so that they understand what you as the teacher are looking for, and how they can be successful. Feedback can be given to students in a variety of ways, a few of which are listed below:

Giulia Forsythe. (2012, November 20). How will students receive feedback? [Graphic]. Retrieved from: link

As you can see, you can give students feedback through written comments on their work, through an audio/video file with your remarks, face-to-face in a conference, and through peer editing or peer feedback. Find a method that works for you and your students, or use a variety of these methods to help students become successful through feedback.

Now that we've talked about ways to give/receive feedback, let's talk about what effective feedback includes. As I mentioned before, some people just give marks and call it a day. For example, this humourous video shows how not to assess students: 

The purpose of assessment is to improve student learning. The feedback we give students should not be vague or give students the correct answer, but give students next steps so that they can be successful next time. If we simply give students the answer, they are not learning anything; we need to lead them in the right direction so that they can figure it out themselves with your guidance.

One of the biggest take-aways from assessment, is the importance of language. We need to be aware of how we give our feedback; it needs to be appropriate, unbiased, positive, and student-friendly. We need to remember that both students and guardians will be reviewing the feedback you give, so be aware of what you say, and how you say it. For example, don't be negative towards a student's answers: "John, this answer sucked, you should have multiplied instead of added the numbers. This answer was mediocre at best, try". This response was negative, unprofessional, used complex language, and gave the student the solution.

Instead, try to say something like: "John, I wonder if you could explain your reasoning for adding? I can see that you added the numbers correctly, good job". This response is positive and praises students for trying to solve the problem. It uses student friendly language, and instead of telling the student what he needed to do correctly, it asks him to explain why he chose this process.

In conclusion, I have learned a lot from this course: be positive about math, ways to differentiate in math, strategies to engage students using technology, and how to give proper feedback. Overall, I think this course has helped me to develop further as a math teacher, and I hope to put this information to good use in my next placement in a few weeks.

Thanks for following me on this journey!

Reflection 5

Last week I talked about differentiated instruction, and types of tasks that are beneficial for learning in the classroom. This week I will talk about integrating technology and using Blended Learning to enhance student learning and engagement. 

Blended Learning is a mixture of face to face instruction and online learning. This type of instruction is most used in post-secondary schooling, but is becoming more common in high school and elementary as technology progresses. It is important to note the distinction between blended learning and tech integration. Technology can (and should) be integrated into the classroom where applicable. It can act as a learning tool, modification, or product for students. This can be the use of iPads, apps, etc. to help students understand the context of a lesson, or to help them create something to show their learning. It does not replace teaching. With Blended Learning, students can control their learning pace, place, and path. They learn online using the technology when, where, and how they want to. This gives our students options and allows for DI for students. 

I was surprised to find out that there are four models for Blended Learning: 

1. Rotation - where students rotate between different learning modes, with at least one is online learning. These modes can include pencil and paper assignments, individual tutoring, group projects, or small group and full class instruction. 
2. Flex - where online learning is the backbone of student learning. Students have an individualized schedule of the different learning modes that they go through at their own pace. Teachers provide face-to-face support as needed. 
3. À-la-carte - where students take courses entirely online with an online teacher, but can still have in-class activities
4. Enriched virtual - where students divide their time between in-class activities and learning online. This differs from À-la-carte because all classes are enriched virtual, and not select classes. 

Personally, I thought that models 3 and 4 where only used in post-secondary education. I know I did some online courses when I was completing my undergrad, but I never thought about them in this way. I hope to try and incorporate a Blended Learning experience in my classroom if I am able. I will be able to do so if I can follow the SAMR Model. 

The SAMR Model is a ladder tool for teachers to follow for integrating technology. It describes what technology can be used for and how it can benefit students. See the model below:

Ruben Puentedura. (2014, September 24). SAMR Model [graphic]. Retrieved from: website

It was interesting to see this model, because a lot of people think that technology can be used the same way as a substitute teacher; teachers get a break from teaching and use technology instead. This is not the case, as you can see. Technology can be used in various ways to enhance learning, and following this model can help teachers use technology appropriately. To understand this model further, view the video below:

 

The Pedagogy Wheel  is a chart that gives apps and other resource examples for each level of the SAMR model for teachers to use. I find it extremely useful, because I often have difficulties coming up with specific apps to use in my lessons. Now that I have this chart, I can explore all these resources and find the ones that I think will best benefit my students. Another good chart for finding technology resources is the Periodic table of iPad apps: 

Mark Anderson. (2014, July 23). iPad Apps [graphic]. Retrieved from: website

Other places to find good technology resources for the classroom include Best websites for teaching and learning and 50 Education technology tools every teacher should know about. For more information about the SAMR model, check out this blog on SAMR and Bloom's Taxonomy by Ruben Puentedura.

I'm really excited about using technology and games to engage students into Math. Gone are the days where students are bored with the same math problems from a textbook. With this information and various resources, I hope to keep my students engaged and excited to learning math.

Reflection 4

Last week we were introduced to parallel tasks. This week we learned about open tasks and rich tasks. Although parallel tasks can be classified as both an open-ended task and a rich task, I have discovered that there are different characteristics to each type of task.

Rich tasks - why are they rich? 
These types of tasks follow certain criteria that allow for deeper thinking in students. These criteria are as follows:

• Allows for range of student abilities and capabilities to solve. 
• Multiple representations can be used to show student thinking based on learning styles and preferences 
• Involves a story or scenario that engages and interests students 
• Connection to real life examples to get students thinking deeply and allows them to see how mathematics can occur in real life situations 
• Promotes student discussion through questioning 
• Enables the use of all 7 mathematical processes
1. Reasoning and proving
2. Selecting tools and computational strategies
3. Representing
4. Connecting
5. Reflecting
6. Communication
7. Problem Solving 

McEachren, Patricia. (2016, September). Halloween Jack-o-lanterns. 

The problem above is an example of a rich task that my professor presented to us. If you compare it to the criteria above, you can see that it is indeed a rich task. I think these types of problems are great for student engagement and to really challenge students. 

Open tasks - how do they promote learning? 

Christopher Danielson. (2013). Which One Doesn't Belong?
[Graphic]. Retrieved from: http://wodb.ca/

These types of tasks give students options, and the opportunity to validate their choice. There will be different answers, but none of the answers that students give are incorrect if they can explain their approach and the strategies they used to solve the problem. I think that these types of tasks promote learning because they give students a chance to think independently and make a choice for themselves. It gets them thinking about their choice and it is accessible to all since they can choose where they want to start. 

In this image, any one of these items can be the one that doesn't belong. It is up to students to decide which one they think doesn't fit based on shape, colour, font, or font colour. As long as students are able to add to the discussion and explain their reasoning, they have succeeded. However, this particular task is not classified as a rich task, because it is not related to math. This series of tasks (Which one doesn't belong) can be found at this site, which asks students which graph, number, shape, and more don't belong. 

Woolley, E. © 2015

This task is an example of an open task word problem. I asked this question to my colleagues during my webinar session on Differentiated Instruction, which I have included below. This particular task is a better example because it is math oriented. As you can see, my peers chose a variety of numbers to work with to solve their problem, which is exactly what we want our students to do. They have a choice on how difficult they make the problem for themselves, so they can challenge themselves based on their abilities.



These types of tasks will be staples in my Math classroom. Not only will the target student interests to get students engaged in mathematics, but they will also challenge them. The great thing about these types of tasks is that it will challenge my students when they solve them, but they will also challenge me to create the problems.

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.